![Page 1: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/1.jpg)
![Page 2: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/2.jpg)
![Page 3: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/3.jpg)
![Page 4: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/4.jpg)
4-1 Statistical Inference
• The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population.
•These methods utilize the information contained in a sample from the population in drawing conclusions.
![Page 5: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/5.jpg)
4-1 Statistical Inference
![Page 6: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/6.jpg)
4-2 Point Estimation
![Page 7: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/7.jpg)
4-2 Point Estimation
![Page 8: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/8.jpg)
4-2 Point Estimation
![Page 9: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/9.jpg)
4-3 Hypothesis Testing
We like to think of statistical hypothesis testing as the data analysis stage of a comparative experiment, in which the engineer is interested, for example, in comparing the mean of a population to a specified value (e.g. mean pull strength).
4-3.1 Statistical Hypotheses
![Page 10: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/10.jpg)
4-3 Hypothesis Testing
For example, suppose that we are interested in the burning rate of a solid propellant used to power aircrew escape systems.
• Now burning rate is a random variable that can be described by a probability distribution.
• Suppose that our interest focuses on the mean burning rate (a parameter of this distribution).
• Specifically, we are interested in deciding whether or not the mean burning rate is 50 centimeters per second.
4-3.1 Statistical Hypotheses
![Page 11: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/11.jpg)
4-3 Hypothesis Testing
4-3.1 Statistical HypothesesTwo-sided Alternative Hypothesis
One-sided Alternative Hypotheses
![Page 12: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/12.jpg)
4-3 Hypothesis Testing
4-3.1 Statistical HypothesesTest of a Hypothesis • A procedure leading to a decision about a particular hypothesis
• Hypothesis-testing procedures rely on using the information in a random sample from the population of interest.
• If this information is consistent with the hypothesis, then we will conclude that the hypothesis is true; if this information is inconsistent with the hypothesis, we will conclude that the hypothesis is false.
![Page 13: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/13.jpg)
4-3 Hypothesis Testing
4-3.2 Testing Statistical Hypotheses
![Page 14: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/14.jpg)
4-3 Hypothesis Testing
4-3.2 Testing Statistical Hypotheses
![Page 15: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/15.jpg)
4-3 Hypothesis Testing
4-3.2 Testing Statistical Hypotheses
Sometimes the type I error probability is called the significance level, or the -error, or the size of the test.
![Page 16: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/16.jpg)
4-3 Hypothesis Testing
4-3.2 Testing Statistical Hypotheses
![Page 17: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/17.jpg)
4-3 Hypothesis Testing
4-3.2 Testing Statistical Hypotheses
![Page 18: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/18.jpg)
4-3 Hypothesis Testing
4-3.2 Testing Statistical Hypotheses
![Page 19: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/19.jpg)
4-3 Hypothesis Testing
4-3.2 Testing Statistical Hypotheses
![Page 20: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/20.jpg)
4-3 Hypothesis Testing
4-3.2 Testing Statistical Hypotheses
![Page 21: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/21.jpg)
4-3 Hypothesis Testing
4-3.2 Testing Statistical Hypotheses
• The power is computed as 1 - , and power can be interpreted as the probability of correctly rejecting a false null hypothesis. We often compare statistical tests by comparing their power properties.
• For example, consider the propellant burning rate problem whenwe are testing H 0 : = 50 centimeters per second against H 1 : not equal 50 centimeters per second . Suppose that the true value of the mean is = 52. When n = 10, we found that = 0.2643, so the power of this test is 1 - = 1 - 0.2643 = 0.7357 when = 52.
![Page 22: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/22.jpg)
4-3 Hypothesis Testing
4-3.3 One-Sided and Two-Sided Hypotheses
Two-Sided Test:
One-Sided Tests:
![Page 23: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/23.jpg)
4-3 Hypothesis Testing
4-3.3 P-Values in Hypothesis Testing
![Page 24: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/24.jpg)
4-3 Hypothesis Testing
4-3.5 General Procedure for Hypothesis Testing
![Page 25: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/25.jpg)
4-4 Inference on the Mean of a Population, Variance Known
Assumptions
![Page 26: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/26.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.1 Hypothesis Testing on the Mean
We wish to test:
The test statistic is:
![Page 27: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/27.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.1 Hypothesis Testing on the Mean
Reject H0 if the observed value of the test statistic z0 is either:
or
Fail to reject H0 if
![Page 28: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/28.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.1 Hypothesis Testing on the Mean
![Page 29: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/29.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.1 Hypothesis Testing on the Mean
![Page 30: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/30.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.2 Type II Error and Choice of Sample Size
Finding The Probability of Type II Error
![Page 31: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/31.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.2 Type II Error and Choice of Sample Size
Sample Size Formulas
![Page 32: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/32.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.2 Type II Error and Choice of Sample Size
Sample Size Formulas
![Page 33: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/33.jpg)
4-4 Inference on the Mean of a Population, Variance Known4-4.2 Type II Error and Choice of Sample Size
![Page 34: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/34.jpg)
4-4 Inference on the Mean of a Population, Variance Known4-4.2 Type II Error and Choice of Sample Size
![Page 35: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/35.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.3 Large Sample Test
In general, if n 30, the sample variance s2 will be close to σ2 for most samples, and so s can be substituted for σ in the test procedures with little harmful effect.
![Page 36: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/36.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.4 Some Practical Comments on Hypothesis Testing
The Seven-Step Procedure
Only three steps are really required:
![Page 37: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/37.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.4 Some Practical Comments on Hypothesis Testing
Statistical versus Practical Significance
![Page 38: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/38.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.4 Some Practical Comments on Hypothesis Testing
Statistical versus Practical Significance
![Page 39: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/39.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.5 Confidence Interval on the Mean
Two-sided confidence interval:
One-sided confidence intervals:
Confidence coefficient:
![Page 40: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/40.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.5 Confidence Interval on the Mean
![Page 41: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/41.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.6 Confidence Interval on the Mean
![Page 42: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/42.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.5 Confidence Interval on the Mean
![Page 43: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/43.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.5 Confidence Interval on the Mean
Relationship between Tests of Hypotheses and Confidence Intervals
If [l,u] is a 100(1 - ) percent confidence interval for the parameter, then the test of significance level of the hypothesis
will lead to rejection of H0 if and only if the hypothesized value is not in the 100(1 - ) percent confidence interval [l, u].
![Page 44: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/44.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.5 Confidence Interval on the Mean
Confidence Level and Precision of Estimation
The length of the two-sided 95% confidence interval is
whereas the length of the two-sided 99% confidence interval is
![Page 45: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/45.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.5 Confidence Interval on the Mean
Choice of Sample Size
![Page 46: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/46.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.5 Confidence Interval on the Mean
Choice of Sample Size
![Page 47: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/47.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.5 Confidence Interval on the Mean
Choice of Sample Size
![Page 48: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/48.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.5 Confidence Interval on the Mean
One-Sided Confidence Bounds
![Page 49: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/49.jpg)
4-4 Inference on the Mean of a Population, Variance Known
4-4.6 General Method for Deriving a Confidence Interval
![Page 50: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/50.jpg)
4-5 Inference on the Mean of a Population, Variance Unknown
4-5.1 Hypothesis Testing on the Mean
![Page 51: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/51.jpg)
4-5 Inference on the Mean of a Population, Variance Unknown
4-5.1 Hypothesis Testing on the Mean
![Page 52: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/52.jpg)
4-5 Inference on the Mean of a Population, Variance Unknown
4-5.1 Hypothesis Testing on the Mean
![Page 53: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/53.jpg)
4-5 Inference on the Mean of a Population, Variance Unknown
4-5.1 Hypothesis Testing on the Mean
Calculating the P-value
![Page 54: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/54.jpg)
4-5 Inference on the Mean of a Population, Variance Unknown
4-5.1 Hypothesis Testing on the Mean
![Page 55: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/55.jpg)
4-5 Inference on the Mean of a Population, Variance Unknown
4-5.1 Hypothesis Testing on the Mean
![Page 56: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/56.jpg)
4-5 Inference on the Mean of a Population, Variance Unknown
4-5.1 Hypothesis Testing on the Mean
![Page 57: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/57.jpg)
4-5 Inference on the Mean of a Population, Variance Unknown
4-5.1 Hypothesis Testing on the Mean
![Page 58: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/58.jpg)
4-5 Inference on the Mean of a Population, Variance Unknown
4-5.2 Type II Error and Choice of Sample Size
Fortunately, this unpleasant task has already been done, and the results are summarized in a series of graphs in Appendix A Charts Va, Vb, Vc, and Vd that plot for the t-test against a parameter for various sample sizes n.
![Page 59: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/59.jpg)
4-5 Inference on the Mean of a Population, Variance Unknown
4-5.2 Type II Error and Choice of Sample Size
These graphics are called operating characteristic (or OC) curves. Curves are provided for two-sided alternatives on Charts Va and Vb. The abscissa scale factor d on these charts is defined as
![Page 60: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/60.jpg)
4-5 Inference on the Mean of a Population, Variance Unknown
4-5.3 Confidence Interval on the Mean
![Page 61: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/61.jpg)
4-5 Inference on the Mean of a Population, Variance Unknown
4-5.3 Confidence Interval on the Mean
![Page 62: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/62.jpg)
4-5 Inference on the Mean of a Population, Variance Unknown
4-5.4 Confidence Interval on the Mean
![Page 63: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/63.jpg)
4-6 Inference on the Variance of a Normal Population
4-6.1 Hypothesis Testing on the Variance of a Normal Population
![Page 64: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/64.jpg)
4-6 Inference on the Variance of a Normal Population
4-6.1 Hypothesis Testing on the Variance of a Normal Population
![Page 65: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/65.jpg)
4-6 Inference on the Variance of a Normal Population
4-6.1 Hypothesis Testing on the Variance of a Normal Population
![Page 66: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/66.jpg)
4-6 Inference on the Variance of a Normal Population
4-6.1 Hypothesis Testing on the Variance of a Normal Population
![Page 67: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/67.jpg)
4-6 Inference on the Variance of a Normal Population
4-6.1 Hypothesis Testing on the Variance of a Normal Population
![Page 68: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/68.jpg)
4-6 Inference on the Variance of a Normal Population
4-6.1 Hypothesis Testing on the Variance of a Normal Population
![Page 69: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/69.jpg)
4-6 Inference on the Variance of a Normal Population
4-6.2 Confidence Interval on the Variance of a Normal Population
![Page 70: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/70.jpg)
4-7 Inference on Population Proportion
4-7.1 Hypothesis Testing on a Binomial Proportion
We will consider testing:
![Page 71: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/71.jpg)
4-7 Inference on Population Proportion
4-7.1 Hypothesis Testing on a Binomial Proportion
![Page 72: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/72.jpg)
4-7 Inference on Population Proportion
4-7.1 Hypothesis Testing on a Binomial Proportion
![Page 73: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/73.jpg)
4-7 Inference on Population Proportion
4-7.1 Hypothesis Testing on a Binomial Proportion
![Page 74: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/74.jpg)
4-7 Inference on Population Proportion
4-7.2 Type II Error and Choice of Sample Size
![Page 75: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/75.jpg)
4-7 Inference on Population Proportion
4-7.2 Type II Error and Choice of Sample Size
![Page 76: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/76.jpg)
4-7 Inference on Population Proportion
4-7.3 Confidence Interval on a Binomial Proportion
![Page 77: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/77.jpg)
4-7 Inference on Population Proportion
4-7.3 Confidence Interval on a Binomial Proportion
![Page 78: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/78.jpg)
4-7 Inference on Population Proportion
4-7.3 Confidence Interval on a Binomial ProportionChoice of Sample Size
![Page 79: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/79.jpg)
4-8 Other Interval Estimates for a Single Sample
4-8.1 Prediction Interval
![Page 80: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/80.jpg)
4-8 Other Interval Estimates for a Single Sample
4-8.2 Tolerance Intervals for a Normal Distribution
![Page 81: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/81.jpg)
4-10 Testing for Goodness of Fit
• So far, we have assumed the population or probability distribution for a particular problem is known.
• There are many instances where the underlying distribution is not known, and we wish to test a particular distribution.
• Use a goodness-of-fit test procedure based on the chi-square distribution.
![Page 82: 4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population](https://reader030.vdocument.in/reader030/viewer/2022032522/56649d625503460f94a445c1/html5/thumbnails/82.jpg)