A machine in the student lounge dispenses coffee. The average cup of coffee is supposed to contain 7.0 ounces. A random sample of nine cups of coffee from this machine show the average content to be 7.3 ounces with a standard deviation of 0.70 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.

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Sketch the sampling distribution and show the area corresponding to the P-value.
2
(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 a?
O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
O At the a = 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.
O There is sufficient evidence at the 0.05 level to conclude that the mean amount of coffee per cup differs from 7 ounces.
O There is insufficient evidence at the 0.05 level to conclude that the mean amount of coffee per cup differs from 7 ounces.
Transcribed Image Text:Sketch the sampling distribution and show the area corresponding to the P-value. 2 (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 a? O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a = 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. O There is sufficient evidence at the 0.05 level to conclude that the mean amount of coffee per cup differs from 7 ounces. O 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 nine cups of coffee from this machine show the average content to be 7.3 ounces with a standard deviation of 0.70 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.
A USE SALT
What are we testing in this problem?
O single proportion
O single mean
(a) What is the level of significance?
State the null and alternate hypotheses.
O Hạ: p = 7; H,:p + 7
O Hg: 4 = 7; H,: H <7
O Hg: p = 7; H,: p > 7
O Hạ: p = 7; H,: p < 7
O Hạ: H = 7; H,: 4 > 7
O Hạ: H = 7; H,: H + 7
(b) What sampling distribution will you use? What assumptions are you making?
O The standard normal, since we assume that x has a normal distribution with known o.
O The Student's t, since n is large with unknown o.
O The standard normal, since we assume that x has a normal distribution with unknown o.
O The Student's t, since we assume that x has a normal distribution with unknown o.
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c) Find (or estimate) the P-value.
O P-value > 0.500
O 0.250 < P-value < 0.500
O 0.100 < P-value < 0.250
O 0.050 < P-value < 0.100
O 0.010 < P-value < 0.050
O P-value < 0.010
Transcribed Image Text:A machine in the student lounge dispenses coffee. The average cup of coffee is supposed to contain 7.0 ounces. A random sample of nine cups of coffee from this machine show the average content to be 7.3 ounces with a standard deviation of 0.70 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. A USE SALT What are we testing in this problem? O single proportion O single mean (a) What is the level of significance? State the null and alternate hypotheses. O Hạ: p = 7; H,:p + 7 O Hg: 4 = 7; H,: H <7 O Hg: p = 7; H,: p > 7 O Hạ: p = 7; H,: p < 7 O Hạ: H = 7; H,: 4 > 7 O Hạ: H = 7; H,: H + 7 (b) What sampling distribution will you use? What assumptions are you making? O The standard normal, since we assume that x has a normal distribution with known o. O The Student's t, since n is large with unknown o. O The standard normal, since we assume that x has a normal distribution with unknown o. O The Student's t, since we assume that x has a normal distribution with unknown o. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) the P-value. O P-value > 0.500 O 0.250 < P-value < 0.500 O 0.100 < P-value < 0.250 O 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 O P-value < 0.010
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