Question

A) Hypothesis Testing - Type I and Type II errors: You test the claim that the mean gas mileage of all cars of a certain make is less than 29 miles per gallon (mpg). You perform this test at the 0.10 significance level. What is the probability of a Type I error for this test?

B)Sleep: Assume the general population gets an average of 7 hours of sleep per night. You randomly select 40 college students and survey them on their sleep habits. From this sample, the mean number of hours of sleep is found to be 6.69 hours with a standard deviation of 0.40 hours. You claim that college students get less sleep than the general population. That is, you claim the mean number of hours of sleep for all college students is less than 7 hours. Test this claim at the 0.01 significance level.
What is the test statistic? Round your answer to 2 decimal places. t_x=

What is the critical value of t? Use the answer found in the t-table or round to 3 decimal places.
t_α =

Answer 1

A) At 10% level of significance we want test the claim that the mean gas mileage of all cars of a certain make is less than 29 miles per gallon.

The probability of type I error, ie probability of rejecting null hypothesis when it is true is:

p=0.10

Since level of significance is the probability of type I error.

B) Given general population gets an average of 7 hours of sleep per night.

A random sample of 40 student is surveyed and found that the mean number of hours of sleep is found to be 6.69 hours with a standard deviation of 0.40 hours.

At 1% level of significance we want to test the claim that the mean number of hours of sleep for all college students is less than 7 hours.

The hypothesis testing problem is

vs

The test statistic is



Here sample size is n=40, therefore the degrees of freedom is 40-1=39

The critical value at 1% level of significance with 39 degrees of freedom for lower tail test is

Tcrit=2.423

Since abs(tx) =4.994>2.423, we reject the null hypothesis at 1% level of significance.

Therefore we have sufficient evidence to claim that the mean number of hours of sleep for all college students get less sleep than the general population.