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 ? ≈ 700 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? (A) single proportion B) single mean (a) What is the level of significance? _________ State the null and alternate hypotheses. (A) H0: ? = 13.5; H1: ? > 13.5 (B) H0: ? = 13.5; H1: ? ≠ 13.5 (C) H0: p = 13.5; H1: p < 13.5 (D) H0: p = 13.5; H1: p > 13.5 (E) H0: p = 13.5; H1: p ≠ 13.5 (F) H0: ? = 13.5; H1: ? < 13.5 (Part 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 unknown ?. (B) The Student's t, since we assume that x has a normal distribution with known ?. (C) The Student's t, since we assume that x has a normal distribution with unknown ?. (D) The standard normal, since we assume that x has a normal distribution with known ?. What is the value of the sample test statistic? (Round your answer to two decimal places.) (Part c) Find (or estimate) the P-value. (A) P-value > 0.500 (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 (Part 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 ?? (A) At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. (B) At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. (C) At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (D) At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (Part 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.

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 ? ≈ 700 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? (A) single proportion B) single mean (a) What is the level of significance? _________ State the null and alternate hypotheses. (A) H0: ? = 13.5; H1: ? > 13.5 (B) H0: ? = 13.5; H1: ? ≠ 13.5 (C) H0: p = 13.5; H1: p < 13.5 (D) H0: p = 13.5; H1: p > 13.5 (E) H0: p = 13.5; H1: p ≠ 13.5 (F) H0: ? = 13.5; H1: ? < 13.5 (Part 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 unknown ?. (B) The Student's t, since we assume that x has a normal distribution with known ?. (C) The Student's t, since we assume that x has a normal distribution with unknown ?. (D) The standard normal, since we assume that x has a normal distribution with known ?. What is the value of the sample test statistic? (Round your answer to two decimal places.) (Part c) Find (or estimate) the P-value. (A) P-value > 0.500 (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 (Part 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 ?? (A) At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. (B) At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. (C) At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (D) At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (Part 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.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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Question

(A) single proportion

B) single mean

(a) What is the level of significance?

_________

State the null and alternate hypotheses.

(A) H₀: ? = 13.5; H₁: ? > 13.5

(B) H₀: ? = 13.5; H₁: ? ≠ 13.5

(C) H₀: p = 13.5; H₁: p < 13.5

(D) H₀: p = 13.5; H₁: p > 13.5

(E) H₀: p = 13.5; H₁: p ≠ 13.5

(F) H₀: ? = 13.5; H₁: ? < 13.5

(Part 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 unknown ?.

(B) The Student's t, since we assume that x has a normal distribution with known ?.

(D) The standard normal, since we assume that x has a normal distribution with known ?.

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

(Part c) Find (or estimate) the P-value.

(A) P-value > 0.500

(B) 0.250 < P-value < 0.500

(D) 0.050 < P-value < 0.100

(E) 0.010 < P-value < 0.050

(F) P-value < 0.010

(Part 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 ??

(A) At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

(B) At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

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

(Part 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.

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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