First we formulate our null and alternate hypotheses:
Ho (null hypothesis) is that the average cup of coffee is 7 ounces
Ha (alternate hypothesis) is that the average cup of coffee is different from 7 ounces
Because the alternate hypothesis is that the average is different from 7 ounces, this is a two-tailed test.
With a sample size of only 8 and an unknown standard deviation, the single mean t-statistic is appropriate here.
For a sample size of 8 and standard deviation of 0.7, the standard error of the mean (7) = 0.7 / square root 8 = 0.247
The t-statistic = sample mean (7.2) - population mean (7)/ standard error of mean (0.247) = 0.809
For a 5% level of significance and a two-tailed test, the associated critical t value at 0.025 (half of the level of significance is used for a two-tailed test) is 2.365.
Using the critical value, |t| > 2.365 to reject Ho at a 5% level of significance. Since that is not true, Ho is not rejected and the claim that the average cup of coffee is supposed to contain 7 ounces is accepted.
The probability of getting a t-statistic as extreme as 0.809, also known as the p-value is 0.774, which is very high, providing additional support for not rejecting the null hypothesis.
