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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?

State the null and alternate hypotheses.

*H*

_{0}: μ = 7;

*H*

_{1}: μ ≠ 7

*H*

_{0}:

*p*= 7;

*H*

_{1}:

*p*< 7

*H*

_{0}: μ = 7;

*H*

_{1}: μ < 7

*H*

_{0}:

*p*= 7;

*H*

_{1}:

*p*≠ 7

*H*

_{0}: μ = 7;

*H*

_{1}: μ > 7

*H*

_{0}:

*p*= 7;

*H*

_{1}:

*p*> 7

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

*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

*P*-value < 0.500

*P*-value < 0.250

*P*-value < 0.100

*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?

(e) Interpret your conclusion in the context of the application.

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