Question

Test the given claim: Assume that a simple random sample is selected from a normally distributed population. Use either the P-value method or the traditional method of testing hypotheses Company A uses a new production method to manufacture aircraft altimeteers. A simple random sample of new altimeters resulted in errors listed below. Use a 0.05 level of significance to test the claim that the new production method has errors with a standard deviation greater than 32.2 ft, which was the standard deviation for the old production method If it appears that the standard deviation is greater, does the new production method appear to be better or worse than the old method? Should the company any action? -41, 79, -20,-73.-41,11,19.54,-8,-52,-109,-109?

1. what is the null and alternative hypotheses?

2. what is the test statistic?

3. what is the critical value

4. is the test between, greater than equal to or less that the critical values

5. do we reject or fail to reject the test

6. is the test less, greater or about the same

7. is the altimeters the same number, fewer or more

8. should the company take action or not take action to reduce the variation

Answer 1

1.The null and alternative hypotheses.

Null hypothesis : The new method and old methods are same ie both the standard deviations are the same.

Alternative Hypothesis: The new production method is better or worse than the old method.

Level of significance:

2. Test Statistic : follows a .

The standard deviation for the new method is

R
-41	1681
79	6241
-20	400
-73	5329
-41	1681
11	121
19.54	381.8116
-8	64
-52	2704
-109	11881
-109	11881
-343.46	42364.81

From the data we calculate the mean=

  

  

  

  

  

  

  

  

  

Test statistic T=30.5165

3. Critical Value:

The Critical value for a two sided Chisquared value the critical values are

or

Therefore the critical values are or

4. is the test between, greater than equal to or less that the critical values

The test is greater than the critical values (30.5165> 20.4833)

5. do we reject or fail to reject the test

Since T(30.5165) is not in the acceptable range (3.2471,20.4833), we reject the test.

6. is the test less, greater or about the same

Since the test is rejected, we accept the alternative that the standard deviation is not equal to the old method. and since the T is more than the upper limit, we conclude that the variance is more.

7.  is the altimeters the same number, fewer or more

The altimeters is more

8. should the company take action or not take action to reduce the variation

The company should take action to reduce the variation if it want to go ahead with the new production method.