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Name: The average annual miles driven per vehicle in the United States is 11
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Description: 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

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.5: The Binomial Theorem

Problem 18E

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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.

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: μ = 11.1; H₁: μ > 11.1

d) H₀: μ = 11.1; H₁: μ ≠ 11.1

e) H₀: p = 11.1; H₁: p ≠ 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 standard normal, 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 Student's t, 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 (or estimate) the P-value.

a) P-value > 0.50

b) 0.250 < P-value < 0.500

c) 0.100 < P-value < 0.250

d) 0.050 < P-value < 0.100

e)0.010 < P-value < 0.050

f) P-value < 0.010

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

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.

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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