Question

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 423.0 gram setting. It is believed that the machine is underfilling the bags. A 39 bag sample had a mean of 422.0 grams. A level of significance of 0.01 will be used. Is there sufficient evidence to support the claim that the bags are underfilled? Assume the standard deviation is known to be 23.0. What is the conclusion?

A) There is not sufficient evidence to support the claim that the bags are underfilled.

B) There is sufficient evidence to support the claim that the bags are underfilled.

Answer 1

 

Population mean = = 423.0

Sample mean = = 422.0

Sample standard deviation = s = 23.0

Sample size = n = 39

Level of significance = = 0.01

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 423.0

Ha: 423.0

The test statistics,

t = ( - )/ (s/)

= ( 422 - 423 ) / ( 23 / 39)

= - 0.272

Critical value of  the significance level is α = 0.01, and the critical value for a two-tailed test is

= 2.712

Since it is observed that |t| = 0.212 < = 2.712 it is then concluded that the null hypothesis is fails to reject.

P- Value = 0.7875

The p-value is p = 0.7875 > 0.01 it is concluded that the null hypothesis is fails 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 population mean μ is different than 423, at the 0.01 significance level.

A)  There is not sufficient evidence to support the claim that the bags are underfilled.