Question

A large food processing company wants to pack exactly 300 grams of tune fish in a can. It is known fro past experience that the weights of the cans have a standard deviation of 5 grams. A sample size of 19 was taken. the sample mean was calculated to be 301?

Answer 1

Solution:

Given: A large food processing company wants to pack exactly 300 grams of tune fish in a can.

that is we have to test if mean

Population  standard deviation =

Sample size= n= 19

Sample mean =

Step 1) State H0 and H1:

Since hypothesis statement is non-directional, this is two tailed test.

Vs

Step 2) Test statistic:

.

Step 3) critical values:

Since level of significance is not given , we use level of significance =

Since this is two tailed, we find : Area =

Look in z table for area = 0.0250 or its closest area and find z value

Area 0.0250 corresponds to -1.9 and 0.06

thus z critical value = -1.96

Since this is two tailed test, we have two z critical values: ( -1.96 , 1.96)

Step 4)  Decision Rule:
Reject null hypothesis ,if z  test statistic value < z critical value=-1.96 or z  test statistic value > z critical value=1.96, otherwise we fail to reject H0.

Since z  test statistic value = 0.87 <  z critical value=1.96, we fail to reject H0.

Step 5) Conclusion:

At 0.05 level of significance, we have sufficient evidence to conclude that: A large food processing company packs exactly 300 grams of tune fish in a can.