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 eight cups of coffee from this machine show the average content to be 7.4 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. What is the value of the sample test statistic? (Round your answer to three decimal places.)

Answer 1

Solution :

Given that,

Population mean = = 7.0

Sample mean = = 7.4

Sample standard deviation = s = 0.70

Sample size = n = 8

Level of significance = = 0.05

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 7.0

Ha: 7.0

The test statistics,

t = ( - )/ (s/)

= ( 7.4 - 7 ) / ( 0.70 / 8)

= 1.616

The value of the sample test statistic is 1.616

p-value = 0.1501

The p-value is p = 0.1501 > 0.05, it is concluded that the null hypothesis is fail to reject.

Conclusion:

It is concluded that the null hypothesis is fail to reject. Therefore there is not enough evidence to claim that the average

amount of coffee per cup is different from 7 ounces. at 0.05 significance level.