Question

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 422 gram setting. It is believed that the machine is underfilling the bags. A 25 bag sample had a mean of 418 grams with a standard deviation of 16. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. State the null and alternative hypotheses.

Answer 1

Solution :

Given that,

Population mean = = 422

Sample mean = = 418

Sample standard deviation = s = 16

Sample size = n = 25

Level of significance = = 0.1

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 422

Ha: 422

The test statistics,

t = ( - )/ (s/)

= ( 418 - 422 ) / ( 16 /25 )

= -1.25

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

= 1.711

Since it is observed that |t| = 1.25 < = 1.711 ,it is then concluded that the null hypothesis is fail to rejected.

P- Value = 0.2234   

The p-value is p = 0.2234 > 0.1, it is concluded that the null hypothesis is fail to rejected.

Conclusion :

It is concluded that the null hypothesis Ho is fail to rejected. Therefore, there is not enough evidence to claim that the bag filling machine works correctly at the 422 gram setting, at the 0.1 significance level.