Question

manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 418 gram setting. Based on a 24 bag sample where the mean is 415 grams and the variance is 225, is there sufficient evidence at the 0.1 level that the bags are underfilled or overfilled? Assume the population distribution is approximately normal.

Step 1 of 5:

State the null and alternative hypotheses

Step 2 of 5:

Find the value of the test statistic. Round your answer to three decimal places.

Step 3 of 5:

Specify if the test is one-tailed or two-tailed.

Step 4 of 5:

Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places

Step 5 of 5:

Make the decision to reject or fail to reject the null hypothesis

.

Answer 1

State the null and alternative hypotheses

Ho:

Ha:

alpha=level of significance=0.1

Find the value of the test statistic. Round your answer to three decimal place

t=xbar-mu/s/sqrt(n)

xbar=sample mean

s=samplesd=sqrt(variance)=sqrt(225)=15

n=sample size=24

=(415-418)/(15/sqrt(24))

t=-0.980

Specify if the test is one-tailed or two-tailed.

its a two tailed test as it is non directional

Determine the decision rule for rejecting the null hypothesis

if p<0.1 reject Ho

if p>0.1 fail to reject H0

here p value ca be found in excel as

=T.DIST.2T(0.98;23)

=0.337282757

=0.337

p=0.337

Step 5 of 5:

Make the decision to reject or fail to reject the null hypothesis

here p=0.337

p>0.1

Fail to reject the null hypothesis.