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A consumer advocacy group is doing a large study on car rental practices. Among other things, the consumer group would like to do a statistical test regarding the mean monthly mileage, μ, of cars rented in the U.S. this year. The consumer group has reason to believe that the mean monthly mileage of cars rented in the U.S. this year is greater than last year's mean, which was 2850 miles.The group plans to do a statistical test regarding the value of μ. It chooses a random sample of monthly mileages and computes the mean of the sample to be 2950 miles and the standard deviation to be 700 miles.Based on this information, answer the questions below.

What are the null hypothesis ( H0 ) and the alternative hypothesis ( H1 ) that should be used for the test? H0 : μ is ?less than,less than or equal to,greater than,greater than or equal to,not equal to,equal to ?700,2850,2950 H1 : μ is ?less than,less than or equal to,greater than,greater than or equal to,not equal to,equal to ?700,2850,2950 In the context of this test, what is a Type II error? A Type II error is ?rejecting,failing to reject the hypothesis that μ is ?less than,less than or equal to,greater than,greater than or equal to,not equal to,equal to ?700,2850,2950 when, in fact, μ is ?less than,less than or equal to,greater than,greater than or equal to,not equal to,equal to ?700,2850,2950. Suppose that the group decides to reject the null hypothesis. What sort of error might it be making??Type I,Type II

Answer 1

(a)
H0 : 2850

H1: 2850

(b)

Type II error is failing to reject the hypothesis that 2850 when , in fact, 2850.

(c)

Suppose that the group decides to reject the null hypothesis. The sort of error might it be making: Type I

Answer 2

The null hypothesis (H0) and the alternative hypothesis (H1) for the test regarding the mean monthly mileage (μ) of cars rented in the U.S. this year can be stated as follows:

H0: μ ≤ 2850 H1: μ > 2850

In this case, the null hypothesis (H0) represents the belief that the mean monthly mileage is less than or equal to 2850 miles, which implies that there has been no increase in the mean monthly mileage compared to last year.

The alternative hypothesis (H1) states that the mean monthly mileage is greater than 2850 miles, indicating that there is an increase in the mean monthly mileage compared to last year.

A Type II error in the context of this test would occur if the consumer group fails to reject the null hypothesis (H0) when, in fact, the mean monthly mileage (μ) is greater than 2850 miles. In other words, the group would conclude that there is no increase in the mean monthly mileage when there actually is one.

If the consumer group decides to reject the null hypothesis (H0), it means they conclude that there is an increase in the mean monthly mileage. In this case, the group might be making a Type I error, which is rejecting the null hypothesis when it is true. It means they would falsely conclude that there is an increase in the mean monthly mileage when there isn't one.

To summarize:

• Type I error: Rejecting the null hypothesis when it is true.

• Type II error: Failing to reject the null hypothesis when it is false.