Posted: July 18th, 2021

What is the level of significance?

 

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The average annual miles driven per vehicle in the United States is 11.1 thousand miles, with σ ≈ 600 miles. Suppose that a random sample of 36 vehicles owned by residents of Chicago showed that the average mileage driven last year was 10.9 thousand miles. Does this indicate that the average miles driven per vehicle in Chicago is different from (higher or lower than) the national average? Use a 0.05 level of significance.

What are we testing in this problem?
A.) single mean
B.) single proportion 

(a) What is the level of significance?

State the null and alternate hypotheses.
A.) H0: p = 11.1; H1: p < 11.1
B.) H0: p = 11.1; H1: p > 11.1 
C.) H0: p = 11.1; H1: p ≠ 11.1
D.) H0: μ = 11.1; H1: μ < 11.1
E.) H0: μ = 11.1; H1: μ ≠ 11.1
F.) H0: μ = 11.1; H1: μ > 11.1

(b) What sampling distribution will you use? What assumptions are you making?
A.) The Student’s t, since we assume that x has a normal distribution with known σ.
B.) The Student’s t, since we assume that x has a normal distribution with unknown σ. 
C.) The standard normal, since we assume that x has a normal distribution with known σ.
D.) The standard normal, since we assume that x has a normal distribution with unknown σ.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

(c) Find the P-value. (Round your answer to four decimal places.)

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
A.) At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
B.) At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. 
C.) At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
D.) At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.
A.) There is sufficient evidence at the 0.05 level to conclude that the miles driven per vehicle in the city differs from the national average.
B.) There is insufficient evidence at the 0.05 level to conclude that the miles driven per vehicle in the city differs from the national average. 

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