Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 411 gram setting. It is believed that the machine is underfilling the bags. A 26 bag sample had a mean of 406 grams with a variance of 225. Assume the population is normally distributed. A level of significance of 0.02 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.

Answer 1

Solution :

Given that,

Population mean = = 411

Sample mean = = 406

Sample standard deviation = s = 15

Sample size = n = 26

Level of significance = = 0.02

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 411

Ha: 411

The test statistics,

t = ( - )/ (s/)

= ( 406 - 411 ) / ( 15 / 26)

= -1.7

df = n - 1 = 25

P- Value = 0.1016   

The p-value is p = 0.1016 > 0.02, it is concluded that the null hypothesis is fails to reject.