Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 425425 gram setting. It is believed that the machine is underfilling the bags. A 1616 bag sample had a mean of 420420 grams with a variance of 256256. A level of significance of 0.0250.025 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.

Reject H0 if t< ?

Answer 1

The claim is the machine is under filling the bags ( i.e Machine fills less than 425 grams )

So , Hypothesis is ,

Η :μ = 425

H, :μ< 425

Left tailed test.

Here population standard deviation ($\sigma$) is not known so we have to use t distribution.

Given , significance level = $\alpha$ = 0.025

Degrees of freedom = n - 1 = 16 - 1 = 15 , where , n is sample size.

So, t critical value for this left tailed test is ,

{ Using Excel function , =T.INV(0.025,15) = -2.131 }

ta,df = 70.025,15 = -2.131

Decision rule for rejecting the null hypothesis :

Reject null hypothesis H₀ if t < -2.131