Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 430 gram setting. It is believed that the machine is overfilling the bags. A 38 bag sample had a mean of 432 grams. Assume the population standard deviation is known to be 29. Is there sufficient evidence at the 0.02 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

Given that a manufacturer of potato chips would like to know whether its bag filling machine works correctly at the = 430 gram setting. It is believed that the machine is overfilling the bags. A n = 38 bag sample had a mean of = 432 grams. Assuming the population standard deviation is known to be = 29.

Step-1

For the given details the hypotheses are:

Step-2:

The test statistic is calculated as:

Z = 0.43

Step-3:

Based on the hypothesis it will be a right-tailed test.

Step-4:

P-value:

The P-value for the calculated test statistic is calculated using excel for normal distribution, the formula is =1-NORM.S.DIST(0.425, TRUE), thus the P-value is 0.3354.

Step-5:

The level of significance is given as 0.02.

Step-6:

Decision:

Since P-value is greater than 0.02 hence we failed to reject the null hypothesis and conclude that there is insufficient evidence to support the claim that the bags are overfilled.