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 26 vehicles owned by residents of Chicago showed that the average mileage driven last year was 10.8thousand 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 proportionsingle mean (a) What is the level of significance?State the null and alternate hypotheses. H0: p = 11.1; H1: p < 11.1H0: p = 11.1; H1: p > 11.1 H0: μ = 11.1; H1: μ ≠ 11.1H0: μ = 11.1; H1: μ > 11.1H0: μ = 11.1; H1: μ < 11.1H0: p = 11.1; H1: p ≠ 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 standard normal, 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. What is the value of the sample test statistic? (Round your answer to two decimal places.)(c) Find the P-value. (Round your answer to four decimal places.)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 vehicle in the city differs from the national average.

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 26 vehicles owned by residents of Chicago showed that the average mileage driven last year was 10.8thousand 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 proportionsingle mean (a) What is the level of significance?State the null and alternate hypotheses. H0: p = 11.1; H1: p < 11.1H0: p = 11.1; H1: p > 11.1 H0: μ = 11.1; H1: μ ≠ 11.1H0: μ = 11.1; H1: μ > 11.1H0: μ = 11.1; H1: μ < 11.1H0: p = 11.1; H1: p ≠ 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 standard normal, 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. What is the value of the sample test statistic? (Round your answer to two decimal places.)(c) Find the P-value. (Round your answer to four decimal places.)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 vehicle in the city differs from the national average.

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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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single proportionsingle mean

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: p = 11.1; H₁: p < 11.1H₀: p = 11.1; H₁: p > 11.1 H₀: μ = 11.1; H₁: μ ≠ 11.1H₀: μ = 11.1; H₁: μ > 11.1H₀: μ = 11.1; H₁: μ < 11.1H₀: p = 11.1; H₁: p ≠ 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 standard normal, 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.

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

(c) Find the P-value. (Round your answer to four decimal places.)

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 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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