- A Random Sample Of Ten Female Students At A High School Were Questioned On How Many Hours Per Week They Watched Televisi 1 (177.93 KiB) Viewed 32 times
- A Random Sample Of Ten Female Students At A High School Were Questioned On How Many Hours Per Week They Watched Televisi 2 (164.12 KiB) Viewed 32 times
A random sample of ten female students at a high school were questioned on how many hours per week they watched television and how many hours per week they used a computer. The responses are shown below together with the difference, d (Computer use – TV use), for each student: Difference Student Computer TV 21 16 2 16 20 15 3 9 4 24 20 5 12 Nao w 18 6 Top 7 9 20 14 15 9 10 You may assume that the differences are Normally distributed. a) Calculate ā, the mean of the differences for these 10 students. 1 3.00 2DP b) The standard deviation of the differences is 3.9721, calculate the standard error of the mean of these paired differences. 1.2561 2 IDP C Using the appropriate multiplier and your answers to a) and b), caleulate the 95% confidence interval for the mean of the paired differences between computer and TV use of students (i.e. 95% CI for pa). Give the lower and upper limits. (i) The lower limit is: 0.159 3DP (ii) The upper limit is: 5841 3D d) From your answers in c) select the appropriate conclusion for your confidence interval:
b) 1.2561 The standard deviation of the differences is 3.9721, calculate the standard error of the mean of these paired differences. c) Using the appropriate multiplier and your answers to a) and b), calculate the 95% confidence interval for the mean of the paired differences between computer and TV use of students (i.e. 95% CI for Md. Give the lower and upper limits. (i) The lower limit is: 1 0.159 3DP (ii) The upper limit is: 5.841 3DP d) From your answers in c) select the appropriate conclusion før your confidence interval: We are 95% confident that the true mean difference between computer usage and television viewing lies between the limits found above; as zero is excluded from the confidence interval there is evidence that computer usage is greater than TV usage. We are 95% confident that the difference between computer usage and television viewing lies between the limits found above; as zero is included in the confidence interval there is evidence of a difference in usage. We are 95% confident that the true mean difference between computer usage and television viewing lies between the limits found above; as zero is excluded from the confidence interval there is evidence that computer usage is lower than TV usage. O We are 95% confident that the true mean difference between computer usage and television viewing lies between the limits found above; as zero is included in the confidence interval there is no evidence of a difference in usage. O We are 95% confident that the difference between computer usage and television viewing lies between the limits found above; as zero is excluded from the confidence interval there is no evidence of a difference in usage.