Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 449 gram setting. It is believed that the machine is underfilling the bags. A 24 bag sample had a mean of 445 grams with a variance of 196. A level of significance of 0.1 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 = = 449

Sample mean = = 445

Sample standard deviation = s = 14

Sample size = n = 24

Level of significance = = 0.1

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 449

Ha: 449

The test statistics,

t = ( - )/ (s/)

= ( 445 - 449 ) / ( 14 / 24 )

= -1.400

Critical value of  the significance level is α = 0.1, and the critical value for a two-tailed test is

= 1.714

Since it is observed that |t| = 1.400 < = 1.714 , it is then concluded that the null hypothesis is fails to reject.

P- Value = 0.1749

The p-value is p = 0.1749 > 0.1, it is concluded that the null hypothesis is fails to reject.