Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 400 400 gram setting. It is believed that the machine is underfilling the bags. A 9 9 bag sample had a mean of 397 397 grams with a standard deviation of 25 25 . A level of significance of 0.025 0.025 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Answer 1

Solution :

= 400

=397

S =25

n = 9

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :    = 400

H_a : < 400

Test statistic = t

= ( - ) / S / n

= (397-400) / 25 / 9

= −0.36

Test statistic = t = −0.36

P-value =0.364

= 0.025  

P-value >

0.364 > 0.025

Fail to reject the null hypothesis .

There is not sufficient evidence to claim that the population mean μ is less than 400, at the 0.025 significance level.