Question

Question 2 Complete both parts (a) and (b). (a). The president of a large chain of fast-food restaurants is interested in estimating the true average net profit among all of their branches over the last year. The net profit (in million euros) from a random sample of 35 branches were recorded and a summary of the responses is shown below: n Minimum Maximum Mean Std. Deviation 1 35 0.12 2.8 1.01 0.58 Net profit (million euros) (i) Provide an interval estimate of the population mean, ?, calculated at the 90% Confidence level, and interpret the result with reference to this application. [5 marks] (ii) The president believes the true average net profit should not be any different than 1 million euro. Would you agree or disagree that the true average net profit for all the branches is a value of 1 million euro. Use the confidence interval calculated in part (i) to justify your answer. [2 marks] (iii) If an interval estimate of ? is desired that is more precise, i.e. narrower, than that calculated in part (i) should this be calculated at a higher or lower confidence level? [1 marks] (b). Another sample of 25 branches were selected for which the last year's drive-through sales were recorded. A summary of the drive-through sales for the 25 branches is as follows: n Minimum Maximum Mean Std. Deviation 1 25 2 9.8 5.38 2.12 Drive-Through Sales (million euros) (i) The president believes the last year's true average drive-through sales among all branches should be more than 4.5 million euros. Is there evidence from this sample that the true average drive-through sales is greater than 4.5 million euros, i.e. test the hypotheses H0 : ? = 4.5 versus Ha : ? > 4.5. Carry out the test at ? = 0.1. Include the calculation of the test statistic, the rejection region for the test statistic and a conclusion. [5 marks] (ii) Provide details of any assumptions that are required to be made in order for the hypothesis test carried out in part (i) to be valid. Do the features of the distribution of the sample of drive-through sales indicated by the boxplot above worry you with respect to the validity of the hypothesis test calculated in part (i)? Give a reason for your answer. [2 marks] (iii) Provide an interval estimate of the population mean, calculating at the 90% Confidence level, and interpret the result with reference to this application. [5 marks] Total: 20 marks

          Question 2

Complete both parts (a) and (b).

(a). The president of a large chain of fast-food restaurants is interested in estimating the true average net profit among all of their branches over the last year. The net profit (in million euros) from a random sample of 35 branches were recorded and a summary of the responses is shown below:

n Minimum Maximum Mean Std. Deviation
1 35 0.12 2.8 1.01 0.58

Net profit (million euros)

(i) Provide an interval estimate of the population mean, ?, calculated at the 90% Confidence level, and interpret the result with reference to this application.
[5 marks]

(ii) The president believes the true average net profit should not be any different than 1 million euro. Would you agree or disagree that the true average net profit for all the branches is a value of 1 million euro. Use the confidence interval calculated in part (i) to justify your answer.
[2 marks]

(iii) If an interval estimate of ? is desired that is more precise, i.e. narrower, than that calculated in part (i) should this be calculated at a higher or lower confidence level?
[1 marks]

(b). Another sample of 25 branches were selected for which the last year's drive-through sales were recorded. A summary of the drive-through sales for the 25 branches is as follows:

n Minimum Maximum Mean Std. Deviation
1 25 2 9.8 5.38 2.12

Drive-Through Sales (million euros)

(i) The president believes the last year's true average drive-through sales among all branches should be more than 4.5 million euros. Is there evidence from this sample that the true average drive-through sales is greater than 4.5 million euros, i.e. test the hypotheses H0 : ? = 4.5 versus Ha : ? > 4.5. Carry out the test at ? = 0.1. Include the calculation of the test statistic, the rejection region for the test statistic and a conclusion.
[5 marks]

(ii) Provide details of any assumptions that are required to be made in order for the hypothesis test carried out in part (i) to be valid. Do the features of the distribution of the sample of drive-through sales indicated by the boxplot above worry you with respect to the validity of the hypothesis test calculated in part (i)? Give a reason for your answer.
[2 marks]

(iii) Provide an interval estimate of the population mean, calculating at the 90% Confidence level, and interpret the result with reference to this application.
[5 marks]

Total: 20 marks

Question 2

Complete both parts (a) and (b).

(a). The president of a large chain of fast-food restaurants is interested in estimating the true average net profit among all of their branches over the last year. The net profit (in million euros) from a random sample of 35 branches were recorded and a summary of the responses is shown below:

n Minimum Maximum Mean Std. Deviation
1 35 0.12 2.8 1.01 0.58

Net profit (million euros)

(i) Provide an interval estimate of the population mean, ?, calculated at the 90% Confidence level, and interpret the result with reference to this application.
[5 marks]

(ii) The president believes the true average net profit should not be any different than 1 million euro. Would you agree or disagree that the true average net profit for all the branches is a value of 1 million euro. Use the confidence interval calculated in part (i) to justify your answer.
[2 marks]

(iii) If an interval estimate of ? is desired that is more precise, i.e. narrower, than that calculated in part (i) should this be calculated at a higher or lower confidence level?
[1 marks]

(b). Another sample of 25 branches were selected for which the last year's drive-through sales were recorded. A summary of the drive-through sales for the 25 branches is as follows:

n Minimum Maximum Mean Std. Deviation
1 25 2 9.8 5.38 2.12

Drive-Through Sales (million euros)

(i) The president believes the last year's true average drive-through sales among all branches should be more than 4.5 million euros. Is there evidence from this sample that the true average drive-through sales is greater than 4.5 million euros, i.e. test the hypotheses H0 : ? = 4.5 versus Ha : ? > 4.5. Carry out the test at ? = 0.1. Include the calculation of the test statistic, the rejection region for the test statistic and a conclusion.
[5 marks]

(ii) Provide details of any assumptions that are required to be made in order for the hypothesis test carried out in part (i) to be valid. Do the features of the distribution of the sample of drive-through sales indicated by the boxplot above worry you with respect to the validity of the hypothesis test calculated in part (i)? Give a reason for your answer.
[2 marks]

(iii) Provide an interval estimate of the population mean, calculating at the 90% Confidence level, and interpret the result with reference to this application.
[5 marks]

Total: 20 marks

Added by Laura W.

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