Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 425 gram setting. It is believed that the machine is underfilling the bags. A 23 bag sample had a mean of 417 grams with a standard deviation of 28. A level of significance of 0.01 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Answer 1

Solution :

Given that,

Population mean = = 425

Sample mean = = 417

Sample standard deviation = s = 28

Sample size = n = 23

Level of significance = = 0.01

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 425

Ha: 425

The test statistics,

t =( - )/ (s /n)

= ( 417 - 425 ) / ( 28 / 23 )

= -1.37

Critical value of  the significance level is α = 0.01, and the critical value for a two-tailed test is

= 2.819

Decision rule is,

| t | > 2.819

Since it is observed that |t| = 1.37 < = 2.819, it is then concluded that the null hypothesis is not rejected.