Answered: matchboxes supposed to have average of…

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

matchboxes supposed to have average of 40 matches/box, with ? = 7. A random sample of 96 matchboxes shows the average number of matches per box to be 42.3. Using a 1% level of significance, can you say that the average number of matches per box is more than 40?

What are we testing in this problem?

A.single mean b. single proportion

What is the level of significance?

State the null and alternate hypotheses. Which one?

H₀: p = 40; H₁: p ≠ 40

H₀: ? ≥ 40; H₁: ? < 40

H₀: p ≤ 40; H₁: p > 40

H₀: p ≥ 40; H₁: p < 40

H₀: ? = 40; H₁: ? ≠ 40

H₀: ? ≤ 40; H₁: ? > 40

What sampling distribution will you use? What assumptions are you making?

A.The Student's t, since we assume that x has a normal distribution with unknown ?.

b.The standard normal, since we assume that x has a normal distribution with known ?. C.The standard normal, since we assume that x has a normal distribution with unknown ?.

d.The Student's t, 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.)

Estimate the P-value.

P-value > 0.250

0.125 < P-value < 0.250
0.050 < P-value < 0.125

0.025 < P-value < 0.050

0.005 < P-value < 0.025

P-value < 0.005

Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??

a.At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

b.At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.

c At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

d.At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

Interpret your conclusion in the context of the application.

A.There is sufficient evidence at the 0.01 level to conclude that the average number of matches per box is now greater than 40.

b.There is insufficient evidence at the 0.01 level to conclude that the average number of matches per box is now greater than 40.

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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