Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 440 gram setting. It is believed that the machine is underfilling or overfilling the bags. A 21 bag sample had a mean of 443 grams with a standard deviation of 11. Assume the population is normally distributed. A level of significance of 0.01 will be used. Specify the type of hypothesis test.

answer can be left tailed test,right tailed test or two tailed test

Answer 1

Solution :

Given that,

Population mean = = 440

Sample mean = = 443

Sample standard deviation = s = 11

Sample size = n = 21

Level of significance = = 0.01

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 440

Ha: 440

The test statistics,

t = ( - )/ (s/)

= ( 443 - 440 ) / ( 11 / 21)

= 1.25

P- Value = 0.2258   

The p-value is p = 0.2258 > 0.01 it is concluded that the null hypothesis is fail to reject.

Conclusion :

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

manufacturer of chocolate chips would like to know whether its bag filling machine works different at the 440 gram setting, at

the 0.01 significance level.