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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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