M12L4 Review

Hypothesis Testing

Is it chance that your best friend continues to roll doubles in a game every turn when you have only rolled doubles once? Or, are they cheating?

If you flip a coin to decide who has to do the dishes each night and your sister continues to win with heads 18 times out of 20, is that possibly chance?

Hypothesis testing will allow us to determine whether it is likely or unlikely that there is bias in a given situation.

Hypothesis Testing Continued

We start with null hypothesis which is sometimes referred to as the hypothesis of "no difference" or "no effect“

We may really expect that our sister is cheating with the coin, but our null hypothesis would assume she is not. Then we can check the data to see if it contradicts our null hypothesis.

In a randomized controlled experiment, the null hypothesis will always be that there is no difference in the value of the variable for the control group and the treatment group.

But how do we know what would be far enough away from the average to not be considered chance? When a statistic is not in the middle 95% of our sample, we

can reject the null hypothesis. To correlate that to a z-score, that would mean our statistic’s

z-score is either 1.96 standard deviations above or below the mean.

If the absolute value of z is less than 1.96, then you do no have enough evidence to reject the null hypothesis.

Pic adjusted from http://jukebox.esc13.net/

REMEMBER…

If a sample contains at least 30 individuals, you can use a z-test to be more precise with your hypothesis testing.

To find the z-value of a statistic for a sample with n individuals, a sample mean of x, a population mean of µ, and a standard deviation σ, we do:

Example 1

A wireless company claims that it will save new customers 25% of what they pay for their current plans with other carriers. In a random sample of 35 new customers, the average amount saved was 23% with a standard deviation of 1.5%.

Example 1 continued

Example 2

A pharmaceutical company claims the drug data set will be 1000. In a test of the claim, the mean among 30 trials is actual 1015, with a standard deviation of 47.

Example 2 continued