Question

Moen has instituted a new manufacturing process for assembling a component. Using the old process, the average assembly time was 4.25 minutes per component. After the new process was in place for 30 days, the quality control engineer took a random sample of fourteen components and noted the time it took to assemble each component. Based on the sample data, the average assembly time was 4.38 minutes, with a standard deviation of .16 minutes. Using a significance level of .02, has the new manufacturing process significantly changed the average assembly time? Do a complete and appropriate hypothesis test.

Step 1 (Hypotheses)

H₀:  (Click to select)snpx-bar???  (Click to select)=??>?<  

H_A:  (Click to select)?x-bar?p?sn  (Click to select)=??>?<  

Step 2 (Decision rule)

Using only the appropriate statistical table in your textbook, the critical value for rejecting H₀ is (Click to select)+-± . (report your answer to 3 decimal places, using conventional rounding rules)

Step 3 (Test statistic)

Using the sample data, the calculated value of the test statistic is (Click to select)+-± . (report your answer to 2 decimal places, using conventional rounding rules)

Step 4 (Evaluate the null hypothesis)

Should the null hypothesis be rejected?  (Click to select)yesno

Step 5 (Practical conclusion)

Has the new manufacturing process significantly changed the average assembly time?  (Click to select)yesno

Using only the appropriate statistical table in your textbook, what is the most accurate statement you can make about the numerical value of the p-value of this hypothesis test?       

Answer:  (provide a one-sentence statement about the p-value)

Answer 1

Step 1:

Hypotheses are:

Step 2:

Here we have following information:

Degree of freedom: df=n-1=13

Test is two tailed so critical values are +/- 2.650

Rejection region:

If t < -2.650 or t > 2.650, reject H0

Step 3:

So test statitics will be

Step 4:

Since t lies in the rejection region so we reject the null hypothesis.

Step 5:

The new manufacturing process has significantly changed the average assembly time.

Answer : yes

The p-value must be less than 0.02.