Listed in the table are speeds (mph) measured on a weekday on a section of freeway. Test the claim that the speeds have a standard deviation of 7 mph at the 1% significance level. Assume that the sample is from a normally distributed population. 68 57 68 64 71 60 68 58 69 56 64 67 What are the correct hypotheses? (Select the correct symbols and values.) H0: Select an answer σ σ² s p̂ μ s² p x̄ ? ≥ = < > ≠ ≤ mph Original claim = Select an answer H₀ H₁ H1: Select an answer p s² σ p̂ x̄ μ σ² s ? < ≤ ≥ ≠ > = mph Enter the critical values, along with the significance level and degrees of freedom χ2χ2(αα,df) below the graph. (Graph is for illustration only. No need to shade.) Test Statistic = (Round to three decimal places.) Decision: Select an answer Accept the alternative hypothesis Accept the null hypothesis Reject the null hypothesis Fail to reject the null hypothesis . Conclusion: Select an answer There is not sufficient evidence to warrant rejection of The sample data supports There is sufficient evidence to warrant rejection of There is not enough evidence to support the claim that the speeds have a standard deviation of 7 mph.

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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Listed in the table are speeds (mph) measured on a weekday on a section of freeway. Test the claim that the speeds have a standard deviation of 7 mph at the 1% significance level. Assume that the sample is from a normally distributed population.

68	57	68
64	71	60
68	58	69
56	64	67

What are the correct hypotheses? (Select the correct symbols and values.)
H₀: Select an answer σ σ² s p̂ μ s² p x̄ ? ≥ = < > ≠ ≤ mph Original claim = Select an answer H₀ H₁

H₁: Select an answer p s² σ p̂ x̄ μ σ² s ? < ≤ ≥ ≠ > = mph

Enter the critical values, along with the significance level and degrees of freedom χ2χ2_(αα,df) below the graph. (Graph is for illustration only. No need to shade.)

Test Statistic = (Round to three decimal places.)

Decision: Select an answer Accept the alternative hypothesis Accept the null hypothesis Reject the null hypothesis Fail to reject the null hypothesis .

Conclusion: Select an answer There is not sufficient evidence to warrant rejection of The sample data supports There is sufficient evidence to warrant rejection of There is not enough evidence to support the claim that the speeds have a standard deviation of 7 mph.

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.

Expert Solution

Step 1

Given that,

Sample size $n = 12$

Sample standard deviation $s = 5.1845$

Step 2

Hypothesis:

$H_{0} : σ = 7$ (That is, the speeds have a standard deviation of 7 mph)

$H_{1} : σ \neq 7$ (That is, the speeds does not have a standard deviation of 7 mph)

Critical value:

The chi square critical value at 11 degrees of freedom and 1% significance level is 24.725.

Test statistic:

$\begin{array}{rcl} χ^{2} & = & \frac{(n - 1) s^{2}}{σ^{2}} \\ = & \frac{(12 - 1) 5 . 1845^{2}}{7^{2}} \\ = & 6.034 \end{array}$

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