Question

Use 4 decimal places in your calculations. Final answers may be approximated to 2 decimal places.

A vending machine dispenses coffee. The average cup of coffee is supposed to contain 7.0
ounces. Eight cups of coffee from this machine show the average content to be 7.3 ounces with a
standard deviation of 0.5 ounce. Using a 5% level of significance, test whether the machine has
slipped out of adjustment and if the average amount of coffee per cup is different from 7 ounces.
a. State the null and alternate hypotheses.
b. Determine the p-value.
c. Interpret your results. Can you conclude that the average amount of coffee per cup is
different from 7 ounces? Explain.

Answer 1

a)

H0: = 7

Ha: 7

b)

Test statistics

t = - / S / sqrt(n)

= 7.3 - 7 / 0.5 / sqrt(8)

= 1.70

From T table,

With test statistics t = 1.70 and df = 7

p-value = 0.1329

Since p-value > 0.05 level, we do not have sufficient evidence to reject H0.

c)

We conclude at 0.05 level that we fail to support the claim that the machine has slipped out of

adjustment and if the average amount of coffee per cup is different from 7 ounces.