Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 426 gram setting. It is believed that the machine is underfilling or overfilling the bags. A 47 bag sample had a mean of 434 grams. Assume the population variance is known to be 900. Is there sufficient evidence at the 0.02 level that the bags are underfilled or overfilled?

Step 1 of 6:

State the null and alternative hypotheses.

Step 2. Find the value of the test statistic. Round your answer to two decimal places.

Step 3. Specify if the test is one-tailed or two-tailed.

Step 4.Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5. Identify the level of significance for the hypothesis test.

Step 6. Enter the conclusion.

Answer 1

Step 1 of 6:

State the null and alternative hypotheses.

: Mean weight of chocolates chps bag

Null hypothesis : Ho :   = 426

Alternative : Ha : 426

Step 2. Find the value of the test statistic

Hypothesized Mean : = 426

Number of bags the sample had :Sample size : n= 47

Sample mean weight : = 434 grams

Population variance : =900

Population standard deviation : = 30

Value of the test statistic = 1.83

Step 3. Specify if the test is one-tailed or two-tailed.

AS Alternate hypothesis has ; Two tailed test:

Step 4.Find the P-value of the test statistic

For two tailed test:

P-value = 0.0672

Step 5. Identify the level of significance for the hypothesis test.

Given,

level of significance: =0.02

Step 6. Enter the conclusion.

As P-Value i.e. is greater than Level of significance i.e (P-value:0.0676 > 0.02:Level of significance); Fail to Reject Null Hypothesis
There is not sufficient evidence to conclude that the bags are underfilled or overfilled