The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box, with ? = 8. A random sample of 90 matchboxes shows the average number of matches per box to be 43.0. 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? single meansingle proportion (a) What is the level of significance? State the null and alternate hypotheses. H0: p = 40; H1: p > 40H0: p = 40; H1: p ≠ 40 H0: p = 40; H1: p < 40H0: ? = 40; H1: ? > 40H0: ? = 40; H1: ? ≠ 40H0: ? = 40; H1: ? < 40 (b) What sampling distribution will you use? What assumptions are you making? The Student's t, since we assume that x has a normal distribution with known ?.The standard normal, since we assume that x has a normal distribution with known ?. The standard normal, since we assume that x has a normal distribution with unknown ?.The Student's t, since we assume that x has a normal distribution with unknown ?. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find (or estimate) the P-value. P-value > 0.2500.125 < P-value < 0.250 0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 < P-value < 0.025P-value < 0.005 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 ?? At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 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 0.01 level to conclude that the average number of matches per box is now greater than 40.There is insufficient evidence at the 0.01 level to conclude that the average number of matches per box is now greater than 40.

The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box, with ? = 8. A random sample of 90 matchboxes shows the average number of matches per box to be 43.0. 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? single meansingle proportion (a) What is the level of significance? State the null and alternate hypotheses. H0: p = 40; H1: p > 40H0: p = 40; H1: p ≠ 40 H0: p = 40; H1: p < 40H0: ? = 40; H1: ? > 40H0: ? = 40; H1: ? ≠ 40H0: ? = 40; H1: ? < 40 (b) What sampling distribution will you use? What assumptions are you making? The Student's t, since we assume that x has a normal distribution with known ?.The standard normal, since we assume that x has a normal distribution with known ?. The standard normal, since we assume that x has a normal distribution with unknown ?.The Student's t, since we assume that x has a normal distribution with unknown ?. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find (or estimate) the P-value. P-value > 0.2500.125 < P-value < 0.250 0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 < P-value < 0.025P-value < 0.005 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 ?? At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 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 0.01 level to conclude that the average number of matches per box is now greater than 40.There is insufficient evidence at the 0.01 level to conclude that the average number of matches per box is now greater than 40.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 3GP

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Question

single meansingle proportion

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: p = 40; H₁: p > 40H₀: p = 40; H₁: p ≠ 40 H₀: p = 40; H₁: p < 40H₀: ? = 40; H₁: ? > 40H₀: ? = 40; H₁: ? ≠ 40H₀: ? = 40; H₁: ? < 40

(b) What sampling distribution will you use? What assumptions are you making?

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

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

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

P-value > 0.2500.125 < P-value < 0.250 0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 < P-value < 0.025P-value < 0.005

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 ??

At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 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 0.01 level to conclude that the average number of matches per box is now greater than 40.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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