4. Mac and Charlie are claiming that their diet will help people lose weight wit

Question

4. Mac and Charlie are claiming that their diet will help people lose weight within a month. In order to estimate the mean weight loss of all customers, they take a sample of 18 dieters and record their weight loss one month after joining the program. The sample mean is 12.5 pounds and the sample standard deviation is 9.2 pounds. Please compute the 95% confidence interval for the population mean. a) Would you use a z-score or a t-score for this confidence interval? (Hint: do you know the population variability?) b) Please identify the degrees of freedom: c) What would your critical t-score be? d) What would your standard error of the mean be?. e) Given that the average weight loss from our sample is 12.5 pounds and the standard error of the mean is 2.1685: Calculate the lower boundary of your confidence interval: Calculate the upper boundary of your confidence interval: f) What is the point estimate for of the population mean? g) How would you summarize this for Mac and Charlie? h) You would use at score of to construct a 95% confidence interval, and a t-score of to construct a 99% confidence interval

Explanation / Answer

e)

CI=x+/-ta/2*SE

CI=12.5+/-2.11*2.1685

CI=7.92 to 17.075 (95% confidence interval)

CI=12.5+/-2.9*2.1685

CI=6.21 to 18.79 (99% confidence interval)

f)

12.5

g)

We are 95% confident that the mean value of the weight loss of dietars is between 7.92 to 17.075 and 99% confident that the mean value of weight loss of dieatars is between 6.21 to 18.79

h)

2.11 (95% confidence interval)

2.9 (99% confidence interval)

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