Based on information from the Federal Highway Administration web site, the average annual miles driven per vehicle in the United States is 13.5 thousand miles. Assume σ ≈ 650 miles. Suppose that a random sample of 41 vehicles owned by residents of Chicago showed that the average mileage driven last year was 13.2 thousand miles. Would 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: p = 13.5; H1: p < 13.5H0: p = 13.5; H1: p ≠ 13.5 H0: μ = 13.5; H1: μ < 13.5H0: μ = 13.5; H1: μ > 13.5H0: p = 13.5; H1: p > 13.5H0: μ = 13.5; H1: μ ≠ 13.5(b) What sampling distribution will you use? What assumptions are you making?The Student's t, since we assume that x has a normal distribution with unknown σ.The standard normal, since we assume that x has a normal distribution with unknown σ. 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 known 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 < 0.5000.100 < P-value < 0.2500.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

Name: Based on information from the Federal Highway Administration web site,
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Description: Based on information from the Federal Highway Administration web site, the average annual miles driven per vehicle in the United States is 13.5 thousand miles. Assume σ ≈ 650 miles. Suppose that a random sample of 41 vehicles owned by residents of Ch

The objective is to test whether that the average miles driven per vehicle in Chicago is different from (higher or lower than) the national average. Let μ be the average miles driven per vehicle in Chicago. we are testing single mean in the problem. Sample mean ,x¯ =13.2 thousand miles = 13.2*1000=13200 miles Population mean ,μ = 13.5 thousand miles = 13.5*1000=13500 miles (a) The level of significance is,α = 0.05 The null hypothesis is that the average miles driven per vehicle in Chicago is not different from the national average. That is,H0: μ = 13500 The alternative hypothesis is that the average miles driven per vehicle in Chicago is different from (higher or lower than) the national average. That is, H1: μ ≠ 13500( claim)(b) The sampling distribution used here is standard normal. The standard normal, since we assume that x has a normal distribution with known σ. Sample Size, n =41 Sample mean,x¯ =13200 Population mean,μ = 13500 Population standard deviation, σ ≈ 650 The test statistic is, C) From the alternative hypothesis , the test is two -tailed test. P value: Thus, the p value < 0.010

Answered: Federal Highway Administration web…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Based on information from the Federal Highway Administration web site, the average annual miles driven per vehicle in the United States is 13.5 thousand miles. Assume σ ≈ 650 miles. Suppose that a random sample of 41 vehicles owned by residents of Chicago showed that the average mileage driven last year was 13.2 thousand miles. Would 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: p = 13.5; H₁: p < 13.5H₀: p = 13.5; H₁: p ≠ 13.5 H₀: μ = 13.5; H₁: μ < 13.5H₀: μ = 13.5; H₁: μ > 13.5H₀: p = 13.5; H₁: p > 13.5H₀: μ = 13.5; H₁: μ ≠ 13.5

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

The Student's t, since we assume that x has a normal distribution with unknown σ.

The standard normal, since we assume that x has a normal distribution with unknown σ.

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 known 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 < 0.250

0.050 < P-value < 0.100

0.010 < P-value < 0.050

P-value < 0.010

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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