Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 450 gram setting. It is believed that the machine is underfilling the bags. A 14 bag sample had a mean of 441 grams with a variance of 169. Assume the population is normally distributed. A level of significance of 0.05 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 = = 450

Sample mean = = 441

Sample standard deviation = s = 13

Sample size = n = 14

Level of significance = = 0.05

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 450

Ha: 450

The test statistics,

t = ( - )/ (s/)

= ( 441 - 450 ) / ( 13 / 14 )

= -2.59

df = n - 1 = 14 - 1 = 13

P- Value = 0.0224