Question

11)

What are the null and alternative hypotheses? بي 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 altimeters. 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 take any action? O A. H:6<32.2 ft H: 0=32.2 ft OC. He: 6 = 32.2 ft H: 6> 322 ft O E. H: 0= 32.2 ft OB. H: 0> 32.2 ft H: 6 = 32.2 ft OD Ho: 6 = 32.2 ft H:6*32.2 ft OF. H: 0+32.2 ft H: 6 = 32.2 ft - 45, 75, -22 -75,- 44, 12, 15, 52, -6, -50,- 109,- 109 NNNNN H.: 032.21 Find the test statistic. x=0 (Round to two decimal places as needed.) Determine the critical value(s). evidence to support the claim that the new production method The critical value(s) is/are - (Use a comma to separate answers as needed. Round to two decimal places as needed.) Since the test statistic is the critical value(s). Ho. There is has errors with a standard deviation greater than 32.2 ft. The variation appears to be than in the past, so the new method appears to be have errors. Therefore, the company take immediate action to reduce the variation. because there will be altimeters that

Answer option

Since the test statistic is (lessthan than. between. greater than. equal to) the critical value {s}, (reject. fail to reject) Ho. There is (insufficient. sufficient) evidence to support the claim that the new production method .

The variation appears to be (about the same. Greater. less) than the past, so the new method appears to be (similar. Better. worse) because there will be ( the same number of. more. fewer) altimeters that

Have rrors. Therefore, the company (should. Should not) take immeadiate action to reduce the variation.

12)

Answer option:

(reject) (Sufficient)

(Fail to reject) (not sufficient)

Answer 1

Dear student, we can provide you with the solution of one type of question at a time.

11)

First we have to find the sample variance and standard deviation

2025 5625 484 5625 1936 144 225 2704 2500 -109 11881 -109 11881 Sum = -306 45066

The sample mean X is computed as follows: -306 X = -1 -25.5 12 Also, the sample variance s2 is --=(*-- (3x)) - 2 =(150 - - ) – 387.545 Therefore, the sample sandartd deviation s is s= 152 = 3387.545 = 58.203

(1) for Null and alternate hypothesis

option C is right since we have to test if the new production method has errors with a standard deviation greater than 32.2

This corresponds to a right-tailed test, for which a Chi-Square test for one population variance will be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.05, and the the rejection region for this right-tailed test is R= {x:x2 > 19.675). (3) Test Statistics The Chi-Squared statistic is computed as follows: x = 1 2 (n-1) s = (12-1). 3387.545 -= 35.94 1036.8 (4) Decision about the null hypothesis = 19.675, it is then concluded that the null hypothesis is Since it is observed that x= 35.94 > X rejected. (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population variance o2 is greater than 1036.8, at the 0.05 significance level.

Test statistic is

X2 = 35.94

The critical value is 19.68

Since the test statistic is greater than the critical value {s}, reject Ho. There is sufficient evidence to support the claim that the new production method.

The variation appears to be Greater than the past, so the new method appears to be worse because there will be more altimeters that have errors. Therefore, the company should take immediate action to reduce variation.

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