Question

A machine in the student lounge dispenses coffee. The average cup of coffee is supposed to contain 7.0 ounces. A random sample of six cups of coffee from this machine show the average content to be 7.3 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 meansingle proportion    

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ = 7; H₁: μ ≠ 7H₀: p = 7; H₁: p > 7    H₀: μ = 7; H₁: μ > 7H₀: μ = 7; H₁: μ < 7H₀: p = 7; H₁: p < 7H₀: 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 unknown σ.The standard normal, since we assume that x has a normal distribution with known 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 > 0.5000.250 < P-value < 0.500    0.100 < P-value < 0.2500.050 < P-value < 0.1000.010 < P-value < 0.050P-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.    

Answer 1

The sample mean is , the sample standard deviation is and sample size is .

We are testing for single mean.

a) The level of significance is .

The null and alternate hypotheses are

b) We are using Student's t distribution.

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

The test statistic is

c)The P-value is

The p-value lies in

0.100 < P-value < 0.2500.050

d) Correct choice is:

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

e) The conclusion is

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