Question

It is necessary for an automobile producer to estimate the number of miles per gallon (mpg) achieved by its cars. Suppose that the sample mean for a random sample of 60 cars is 29.4 mpg and assume the standard deviation is 2.2 mpg. Now suppose the car producer wants to test the hypothesis that μ, the mean number of miles per gallon, is not 28.9. Conduct a test using a significance level of α=.05 by giving the following:

(a) The test statistic

(b) The P -value (c)

The final conclusion is A. There is not enough evidence to support the claim. B. There is enough evidence to support the claim.
The time needed for college students to complete a certain paper-and-pencil maze follows a normal distribution with a mean of 30 seconds and a standard deviation of 4 seconds. You wish to see if the mean time μ is changed by vigorous exercise, so you have a group of 15 college students exercise vigorously for 30 minutes and then complete the maze. It takes them an average of x¯=27.1 seconds to complete the maze. Use this information to test the hypotheses
H0:μ=30
Ha:μ≠30
Conduct a test using a significance level of α=0.01.

(a) The test statistic

(b) The positive critical value, z0 =

(c) The final conclusion is

Answer 1

To evaluate the manufacturers' claim about the mean miles per gallon (mpg) of non-hybrid sedans, a hypothesis test can be conducted. The null hypothesis (H0) is that the mean mpg of non-hybrid sedans is greater than or equal to the mean mpg of hybrid sedans. The alternative hypothesis (Ha) is that the mean mpg of non-hybrid sedans is less than the mean mpg of hybrid sedans.

Step-by-step explanation:

To conduct a hypothesis test to evaluate the manufacturers' claim, we need to test whether the mean miles per gallon (mpg) of non-hybrid sedans is actually lower than that of hybrid sedans. The null hypothesis (H0) is that the mean mpg of non-hybrid sedans is greater than or equal to the mean mpg of hybrid sedans. The alternative hypothesis (Ha) is that the mean mpg of non-hybrid sedans is less than the mean mpg of hybrid sedans.

To conduct the hypothesis test, we use the formula for the test statistic: test statistic = (sample mean 1 - sample mean 2) / sqrt((sample variance 1 / sample size 1) + (sample variance 2 / sample size 2))

The test statistic follows a t-distribution with degrees of freedom equal to the smaller of (sample size 1 - 1) or (sample size 2 - 1). We compare the test statistic to the critical value(s) from the t-distribution to determine the p-value.

If the p-value is less than the significance level (alpha), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean mpg of non-hybrid sedans is lower than that of hybrid sedans. If the p-value is greater than alpha, we fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim.