Question

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 31 vehicles owned by residents of Chicago showed that the average mileage driven last year was 10.8 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?

single meansingle proportion     

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ = 11.1; H₁:  μ ≠ 11.1H₀: μ = 11.1; H₁:  μ < 11.1     H₀: p = 11.1; H₁:  p ≠ 11.1H₀: p = 11.1; H₁:  p > 11.1H₀: p = 11.1; H₁:  p < 11.1H₀: μ = 11.1; H₁:  μ > 11.1

(b) What sampling distribution will you use? What assumptions are you making?

The standard normal, since we assume that x has a normal distribution with known σ.The Student's t, since we assume that x has a normal distribution with unknown σ.     The Student's t, since we assume that x has a normal distribution with known σ.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 (or estimate) the P-value.

P-value > 0.5000.250 < P-value < 0.500     0.100 < P-value < 0.2500.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

Sketch the sampling distribution and show the area corresponding to the P-value.

(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?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.     At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.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.

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.There is insufficient evidence at the 0.05 level to conclude that the miles driven per v

Answer 1

level of significance = 0.05

This is the two tailed test .

The null and alternative hypothesis is

H₀ : $\mu$ = 11.1

H_a : $\mu$ $\neq$ 11.1

Test statistic = z

= ($\bar x$ - $\mu$ ) / $\sigma$    / $\sqrt$ n

= (10.8 - 11.1) / 0.6 / $\sqrt$ 31

Test statistic = -2.78

P-value = 0.0054

P-value < 0.010

Graph 4

(d)

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant

(e)

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.