Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 446 gram setting. It is believed that the machine is overfilling the bags. A 33 bag sample had a mean of 452 grams. Assume the population variance is known to be 676. Is there sufficient evidence at the 0.1 level that the bags are overfilled?

Step 1 of 6: State the null and alternative hypotheses.

Step 2 of 6:

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

Step 3 of 6:

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

Step 4 of 6:

Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 6:

Identify the level of significance for the hypothesis test.

Step 6 of 6:

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

Answer 1

The values given in the question are

This is the null hypothesis mean.

Step 1 of 6: State the null and alternative hypotheses.

VS

Step 2 of 6:

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

Test Statistics =

=  

Step 3 of 6:

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

Since this alternative hypo has '>' this means that we are only checking in one direction that is population mean is greater than null hypo mean

Test is

Step 4 of 6:

Find the P-value of the test statistic. Round your answer to four decimal places.

We will use normal distribution since we are testing for population mean and we have population variance given.

p - value = P (Z > T.S.) ..........T.S. is the z-score

= 1 - P(Z < T.S.) ...since we have less than probabilities for normal distribtuion

= 1 - 0.9075 = 0.092

Step 5 of 6:

Identify the level of significance for the hypothesis test.

Level of significance is

Step 6 of 6:

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

p-value is the probability of hypothesis being true so if this is less than the level of acceptance (significance) we would reject the null hypothesis

Since p-value < 0.1

We reject the null hypothesis

We conclude at 0.1 level of significance the bags are overfilled.