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.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 7PPS
Related questions
Topic Video
Question
100%
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.
(b) What sampling distribution will you use? What assumptions are you making?
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c) Find (or estimate) the P-value.
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?
(e) Interpret your conclusion in the context of the application.
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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 4 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill