A machine in the student lounge dispenses coffee. The average cup of coffee is supposed to contain 7.0 ounces. A random sample of seven cups of coffee from this machine show the average content to be 7.2 ounces with a standard deviation of 0.40 ounce. Do you think that the machine has slipped out of adjustment and that the average amount of coffee per cup is different from 7 ounces? Use a 5% level of significance. What are we testing in this problem? single proportion single mean (a) What is the level of significance? State the null and alternate hypotheses. H0: μ = 7; H1: μ ≠ 7 H0: p = 7; H1: p < 7 H0: μ = 7; H1: μ < 7 H0: p = 7; H1: p ≠ 7 H0: μ = 7; H1: μ > 7 H0: p = 7; H1: p > 7 (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 unknown σ.The Student's t, since n is large with unknown σ. The standard normal, since we assume that x has a normal distribution with known σ.The standard normal, since we assume that x has a normal distribution with unknown σ. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) the P-value. P-value > 0.500 0.250 < P-value < 0.500 0.100 < P-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010 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 mean amount of coffee per cup differs from 7 ounces. There is insufficient evidence at the 0.05 level to conclude that the mean amount of coffee per cup differs from 7 ounces.

A machine in the student lounge dispenses coffee. The average cup of coffee is supposed to contain 7.0 ounces. A random sample of seven cups of coffee from this machine show the average content to be 7.2 ounces with a standard deviation of 0.40 ounce. Do you think that the machine has slipped out of adjustment and that the average amount of coffee per cup is different from 7 ounces? Use a 5% level of significance. What are we testing in this problem? single proportion single mean (a) What is the level of significance? State the null and alternate hypotheses. H0: μ = 7; H1: μ ≠ 7 H0: p = 7; H1: p < 7 H0: μ = 7; H1: μ < 7 H0: p = 7; H1: p ≠ 7 H0: μ = 7; H1: μ > 7 H0: p = 7; H1: p > 7 (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 unknown σ.The Student's t, since n is large with unknown σ. The standard normal, since we assume that x has a normal distribution with known σ.The standard normal, since we assume that x has a normal distribution with unknown σ. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) the P-value. P-value > 0.500 0.250 < P-value < 0.500 0.100 < P-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010 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 mean amount of coffee per cup differs from 7 ounces. There is insufficient evidence at the 0.05 level to conclude that the mean amount of coffee per cup differs from 7 ounces.

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Description: A machine in the student lounge dispenses coffee. The average cup of coffee is supposed to contain 7.0 ounces. A random sample of seven cups of coffee from this machine show the average content to be 7.2 ounces with a standard deviation of 0.40 ounce

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 proportion

single mean

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: μ = 7; H₁: μ ≠ 7

H₀: p = 7; H₁: p < 7

H₀: μ = 7; H₁: μ < 7

H₀: p = 7; H₁: p ≠ 7

H₀: μ = 7; H₁: μ > 7

H₀: p = 7; H₁: p > 7

(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 unknown σ.The Student's t, since n is large with unknown σ. The standard normal, since we assume that x has a normal distribution with known σ.The standard normal, since we assume that x has a normal distribution with unknown σ.

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

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

P-value > 0.500

0.250 < P-value < 0.500

0.100 < P-value < 0.250

0.050 < P-value < 0.100

0.010 < P-value < 0.050

P-value < 0.010

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 mean amount of coffee per cup differs from 7 ounces.

There is insufficient evidence at the 0.05 level to conclude that the mean amount of coffee per cup differs from 7 ounces.

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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