A B C D Confidence Interval for the Population Proportion 2 3 Project Description: The present study shows data collected from customers of a gym regarding their satisfaction with the current working hours of the gym. The manager of the gym would like to determine whether his customers are satisfied with the working hours or if the hours should be extended. 285 customers in a random sample were asked whether they were "satisfied" or "dissatisfied" with the working hours. We will find the sample proportion for satisfied customers and use it to build a confidence interval to estimate the true proportion of the population. We will find values from the probability table using Excel functions to build confidence intervals using different confidence levels. We will use the confidence intervals to make conclusions about the population. We will also analyze the width of the confident intervals. We will determine the sample size at a desired level of confidence and margin of error. 6 Instructions: Use a cell reference or a single formula where appropriate in order to receive full credit. Do not copy and paste values or type values, as you will not receive full credit for your answers. For the purpose of grading the project, you are required to perform the following tasks: 8 Points Step Instructions 9 Possible 10 Start Excel. Download and open the workbook named: 0 11 Confidence Intervals for the Population Proportion Start 12 In cell B3, find the number of customers who are "Satisfied" in the Data sheet. 13 2 4 14 Hint: use the COUNTIF function. 15 In cell B4, find the sample size of the sample of customers who responded in the Data sheet. 16 3 4 17 Hint: use the COUNTA function. 18 4 In cell B5, find the proportion of customers who are satisfied. 4 19 In cell B6, find the standard error of the proportion. 20 5 4 21 Hint: Use the formula standard deviation = sqrt(p*(1-p)). 22 6 To build the confidence interval for the proportion of satisfied customers on the Data sheet, what is the appropriate probability table to use? Choose the correct answer from the dropdown 4 menu in cell B7. 23 In cell B8, find the value from the appropriate probability table to construct a 90% confidence interval. 24 7 5 25 Hint: use the NORM.S.INV function. 26 8 In cell B9, find the margin of error at 90% confidence level. 27 In cell B10, find the upper limit for the population proportion at 90% confidence level. 28 10 In cell B11, find the lower limit for the population proportion at 90% confidence level. 29 11 Based on the numbers in cell B9 and B10, we can be 90% confident that: Choose the correct answer from the dropdown menu in cell B12. 30 12 In cell B13, find the width of the confidence interval at 90% confidence level. 31 13 In cell B14, find the value from the appropriate probability table to construct a 99% confidence interval.30 In cell B13, find the width of the confidence interval at 90% confidence level. 31 13 In cell B14, find the value from the appropriate probability table to construct a 99% confidence interval. 32 14 In cell B15, find the margin of error at 99% confidence level. 33 15 In cell B16, find the upper limit for the population proportion at 99% confidence level. 5 34 16 In cell B17, find the lower limit for the population proportion at 99% confidence level. 5 35 17 In cell B18, find the width of the confidence interval at 99% confidence level. 36 18 By comparing the width of the confidence interval (CI) at 90% and 99%, what can we conclude about the width of the CI? Choose the correct answer from the dropdown menu in cell B19. 5 37 19 Based on the upper and lower limit values for a 90% confidence level, can the gym's manager be 90% confident that 90% of his customers are satisfied? Choose the correct answer from the 5 dropdown menu in cell B20. 20 Based on the upper and lower limit values for a 99% confidence level, can the gym's manager be 99% confident that 90% of his customers are satisfied? Choose the correct answer from the 38 dropdown menu in cell B21. 5 39 21 What can the gym manager do to reduce the margin of error at 99% confidence interval? Choose the correct answer from the dropdown menu in cell B22. 5 40 In cell B23, find the required sample size to estimate the true proportion of satisfied customers within 3% margin of error, with 99% confidence. 41 22 5 42 Hint: use the formula n = 0.25*(z_(alpha/2) / margin of error)~2. 43 23 Save your file and submit for grading. 0 AA Total Score 100 45A B C Confidence Interval for the Population Proportion Use a cell reference or a single formula where appropriate in order to receive full credit. Do not copy and paste values or type values, as you will not receive full credit for your answers. 1-2. In cell B3, find the number of customers who are "Satisfied" from the Data sheet. 3. In cell B4, find the sample size of the sample of customers who responded from the Data sheet. 4. In cell B5, find the proportion of customers who are satisfied. 5. In cell B6, find the standard error of the proportion. 6. To build the confidence interval for the proportion of satisfied customers from the Data sheet, what is the appropriate probability table to use? 7. In cell B8, find the value from the appropriate probability table to construct a 90% confidence interval. 8. In cell B9, find the margin of error at 90% confidence level. 9. In cell B10, find the upper limit for the population proportion at 90% confidence level. 1 10. In cell B1 1, find the lower limit for the population proportion at 90% confidence level. 11. Based on the numbers in cell B9 and B10, we can be 90% confident that 12. In cell B13, find the width of the confidence interval at 90% confidence level. 4 13. In cell B14, find the value from the appropriate probability table to construct a 99% confidence interval. 5 14. In cell B15, find the margin of error at 99% confidence level. 6 15. In cell B16, find the upper limit for the population proportion at 99% confidence level. 7 16. In cell B17, find the lower limit for the population proportion at 99% confidence level. 17. In cell B18, find the width of the confidence interval at 99% confidence level 9 18. By comparing the width of the confidence interval (CI) at 90% and 99%, what can we conclude about the width of the CI? 19. Based on the upper and lower limit values for a 90% confidence level, can the gym's manager be 90% confident that 90% of his customers are satisfied? 20. Based on the upper and lower limit values for a 99% confidence level, can the gym's manager be 99% confident that 90% of his customers are satisfied? 21. What can the gym manager do to reduce the margin of error at 99% confidence interval? 22. In cell B23, find the required sample size to estimate the true proportion of satisfied customers within 3% margin of error, with 99% confidence
