business statistics - part 2

8/7/2019 Business Statistics - Part 2

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Paper I & 11

Answer All questions

1. A student is investigating the relationship between the price ( y pence) of 100g of chocolate

and the percentage (x%) of cocoa solids in the chocolate.

The following data is obtained

(a) On the graph paper on page 9 draw a scatter diagram to represent these data. (3)

The student believes that a linear relationship of the form y =a + bx could be used todescribe these data.

(b) Use linear regression to find the value ofa and the value ofb, giving your answers to

one decimal place.(4)(c) Draw the regression line on your scatter diagram.(2)

The student believes that one brand of chocolate is overpriced.

(d) Use the scatter diagram to(i) state which brand is overpriced,(ii) Suggest a fair price for this brand. Give reasons for both your answers.(3)

(e) Explain the use of Correlation and regression studies in Busainess? (3)

(Total Marks 15)


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2. An engineering company manufactures an electronic component. At the end of the

manufacturing process, each component is checked to see if it is faulty. Faulty components are

detected at a rate of 1.5 per hour.

(a) Suggest a suitable model for the number of faulty components detected per hour.(1)

(b) Describe, in the context of this question, two assumptions you have made in part (a) for this

model to be suitable.(2)

(c) Find the probability of 2 faulty components being detected in a 1 hour period.(1)

(d) Find the probability of at least one faulty component being detected in a 3 hour

period.(2)

(e) Write down the conditions under which the Poisson distribution may be used as an

approximation to the Binomial distribution.(2)

A call centre routes incoming telephone calls to agents who have specialist knowledge to deal

with the call. The probability of the caller being connected to the wrong agent is 0.01

(f) Find the probability that 2 consecutive calls will be connected to the wrong agent. (1)

(g) Find the probability that more than 1 call in 5 consecutive calls are connected to the wrongagent. (2)

The call centre receives 1000 calls each day.

(h) Find the mean and variance of the number of wrongly connected calls.(2)

(i) Use a Poisson approximation to find, to 3 decimal places, the probability that more than 6calls each day are connected to the wrong agent.(2)

(Total Marks 15)

3. It is known from past records that 1 in 5 bowls produced in a pottery have minor defects. Tomonitor production a random sample of 25 bowls was taken and the number of such bowls with

defects was recorded.(a)Using a 5% level of significance, find critical regions for a two-tailed test of the

hypothesis that 1 in 5 bowls have defects. The probability of rejecting, in either tail,should be as close to 2.5% as possible. (6)

(b) State the actual significance level of the above test.(1)

At a later date, a random sample of 20 bowls was taken and 2 of them were found to have

defects.c) Test, at the 10% level of significance, whether or not there is evidence that the

proportion of bowls with defects has decreased. State your hypotheses clearly. .(8)

(Total Marks 15)


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The quality control system in the factory identifies and destroys every faulty DVD at theend of the manufacturing process. It costs 0.70 to manufacture a DVD and the factory sells non-

faulty DVDs for 11.(f) Find the expected profit and Variance made by the factory per day.(4)

(Total Marks 15)

4.


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The owner of a small restaurant decides to change the menu. A trade magazine claims that 40%

of all diners choose organic foods when eating away from home. On a randomly chosen day

there are 20 diners eating in the restaurant.

(d) Assuming the claim made by the trade magazine to be correct, suggest a

suitable model to describe the number of diners X who choose organic foods. (2)

(e) Find the mean and standard deviation of X.(3)

The owner decides to survey her customers before finalising the new menu. She surveys 10

randomly chosen diners and finds 8 who prefer eating organic foods.

(f) Test, at the 5% level of significance, whether or not there is reason to believe that the

proportion of diners in her restaurant who prefer to eat organic foods is higher than the trade

magazines claim. State your hypotheses clearly.(6)

(Total Marks 15)

5. Explain what you understand by

(a) a population,(1)

(b) a statistic.(2)

(c) Discuss the importance of sampling in business (3)

A questionnaire concerning attitudes to classes in a college was completed by a random sample

of 50 students. The students gave the college a mean approval rating of 75%.

(c) Identify the population and the statistic in this situation.(2)

(d) Explain what you understand by the sampling distribution of this statistic.(2)

(Total Marks 10)


5/5

(Total Marks 15)

Prepared by

P.Suthaharan BBA(Marketing) (Col)

business statistics - part 2

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