Question

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? what is the test statistic ?

What are the null and alternative hypotheses? Tost 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? - 41, 79, -22. - 71, -42, 13, 18, 53, -6, -50,- 1071075 O A. Ho > 322 H, a=322 © Họ < 32 2 || Hy 3221 OE H = 32211 Hy a < 322 OB. Hy #32 2 Hy a = 322 O. Hy = 3221 Hy >322 OF HO = 322 ft H, #32 2t Find the test statistic (Round to two decimal places as needed.)

Answer 1

Solution Given data -41 79,-22, -7, -42, 13, 18, 53, -6, -50% -607,-107 n=12 Now to find Sample mean D x = x -4 1479 -22-71-42 413+ 18+ 53-6-50-107-107 - 283 12 X = -23.583 Now to find the sample standard deviation 5= {(xi-x)?

Sample standard deviation Now to find the S= n-1 (-41+23.593) + (179423.583) + (-22 +23.583) 671423.583)2 (-48+ 23.583) + (13723.583) +(18723.583) # /53423.583)? H(-6723.582)+(-50+23.583) + (-107+23.58 274 (107723.583)2 37272.9167 fe 5= 3388.4470 S= 58.210 hypothesis, Now to state the null and alternative Null hypothesis Hoi = 32.2 ft Alternative hypothesis H. : - 732.2 A

3 * Now to find the test statistic, x²: We know that The formula of x² statistic is given by 2 x ² (n-1) 5² 2 9 2² (12-1) (58.280) ? X (32.2) () (3388.4040) 1036.84 37272.4451 Х 1036.84 x = 35.95