Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 408 gram setting. Based on a 26 bag sample where the mean is 413 grams and the variance is 625 , is there sufficient evidence at the 0.05 level that the bags are overfilled? Assume the population distribution is approximately normal. Step 2 of 5 : Find the value of the test statistic. Round your answer to three decimal places.

Answer 1

Solution :

Given that,

Step 1 of 5 :

This a right (One) tailed test.

The null and alternative hypothesis is,  

Ho: 408

Ha: 408

Step 2 of 5 :

The test statistics,

t =( - )/ (s /n)

= ( 413 - 408 ) / ( 25 / 26 )

= 1.020

Step 3 of 5 :

P- Value =  0.1587

The p-value is p = 0.1587 > 0.05, it is concluded that the null hypothesis is not rejected.

Step 4 of 5 :

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the bags are overfilled, at the 0.05 significance level.