6. A 2009 study indicated that large population of Canadian doctors reported, on average, a total of muknot= 281 minutes per week of exercise with a standard deviation of sigma= 14.53 minutes per week. Today, you take a random sample of n=20 doctors in Canada, and ask them to report their minutes of exercise per week, and find a sample mean of xbar 287.25 minutes per week.

a) (6m) Create a 90% confidence interval for the average weekly minutes of exercise of doctors in Canada today. At the 10% significance level, is there evidence that the average weekly minutes of exercise for Canadian doctors has changed from 281 minutes? Fill in the table and the brackets below. Z PROBLEM

Conf Level	Signif Level	Conf Interval
Summary Statement	We can be 90% confident that
English Statement (Choose answer)	At the 10% level of significance, because 281 minutes is (inside, outside) the 90% confidence interval, there (is, is not) significant evidence that the average weekly minutes of exercise for Canadian doctors has changed from 281 minutes.

b) (3m) Fully and completely state the two assumptions that must be met to perform the one sample Z confidence interval test above.

1.

2.

c) (7m) Indicate whether each of the following statements is true or false.

i. 90% of doctors exercise weekly for the number of minutes between the endpoints of your interval above.
ii. The width of a 99% Confidence Interval created from the data above would be larger than the width of a 90% CI.
iii. PAGE 3 The shape of a population distribution is always the same as the shape of a test statistic distribution.
iv. There is a probability of 90% that the true mean of weekly doctor exercise minutes is in the 90% confidence interval created above.
v. A 90% confidence interval created from a sample of size 1000 from the population of weekly doctor exercise minutes would have a greater chance of capturing the true mean of weekly doctor exercise minutes than the 90% confidence interval you created with the sample of size 20 above.
vi. 90% of all intervals created with this formula with many many repeated samples of the same size from the population of weekly doctor exercise minutes will contain the true mean of weekly doctor exercise minutes.
vii. Today, we can be sure that the true mean of weekly doctor exercise minutes is 281 minutes.

d)(10m) Perform a hypothesis test to determine if there is evidence that the average weekly minutes of exercise for Canadian doctors has changed from 281 minutes. Use a level of significance of 10%. Fill in and choose answers in brackets.

Hypotheses	Test stat/df	P-value statement and p-value	Decision and Reason	Decision in "English"
Ho: Ha:	z* =