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 emrors 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 are the null and alternative hypotheses? A. Ho o = 32.2 ft O B. H o= 32.2 ft H,: o> 32.2 ft H,: o+ 32.2 ft O C. Ho< 32.2 ft H,: o = 32.2 ft OD. H a= 32.2 ft H,:o<32.2 ft -43, 79, - 25, - 75, -42, 10, 16, 53, -9, - 52, - 106, - 106 O O E. H o 32.2 ft H,: a = 32.2 ft O.F. Ho o>32.2 ft H,: o = 32.2 ft Find the test statistic. 2=36.62 (Round to two decimal places as needed.) Determine the critical value(s). The critical value(s) islare 19.68. (Use a comma to separate answers as needed. Round to two decimal places as needed.). Since the test statistic is greater than the critical value(s). reject Ho. There is sufficient support the claim that the new production method has errors with a standard deviation greater than 32.2 ft. evidence to e variation appears to be v than in the past, so the new method appears to be . because ulere will be V altimeters that have errors. Therefore, the company take immediate action to reduce the variation.
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 emrors 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 are the null and alternative hypotheses? A. Ho o = 32.2 ft O B. H o= 32.2 ft H,: o> 32.2 ft H,: o+ 32.2 ft O C. Ho< 32.2 ft H,: o = 32.2 ft OD. H a= 32.2 ft H,:o<32.2 ft -43, 79, - 25, - 75, -42, 10, 16, 53, -9, - 52, - 106, - 106 O O E. H o 32.2 ft H,: a = 32.2 ft O.F. Ho o>32.2 ft H,: o = 32.2 ft Find the test statistic. 2=36.62 (Round to two decimal places as needed.) Determine the critical value(s). The critical value(s) islare 19.68. (Use a comma to separate answers as needed. Round to two decimal places as needed.). Since the test statistic is greater than the critical value(s). reject Ho. There is sufficient support the claim that the new production method has errors with a standard deviation greater than 32.2 ft. evidence to e variation appears to be v than in the past, so the new method appears to be . because ulere will be V altimeters that have errors. Therefore, the company take immediate action to reduce the variation.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text:The image contains a problem statement for testing a statistical claim using hypothesis testing. Here’s a detailed transcription and explanation suitable for an educational website:
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**Problem Statement:**
A simple random sample from a normally distributed population is selected. Use either the P-value method or the traditional method of testing hypotheses.
**Scenario:**
Company A employs a new production method to manufacture aircraft altimeters, and a simple random sample of new altimeters yielded errors as follows:
- Errors: -43, 79, -25, -75, -42, 10, 16, 53, -9, -52, -106, -106
**Objective:**
Using a significance level of 0.05, test if the new production method results in errors with a standard deviation greater than 32.2 ft. The standard deviation for the old production method was 32.2 ft. Decide if the new production method is better or worse and if the company should take action.
**Hypotheses:**
Select the appropriate null and alternative hypotheses:
- (A) \( H_0: \sigma = 32.2 \) ft, \( H_1: \sigma > 32.2 \) ft
- (B) \( H_0: \sigma = 32.2 \) ft, \( H_1: \sigma < 32.2 \) ft
- (C) \( H_0: \sigma = 32.2 \) ft, \( H_1: \sigma \neq 32.2 \) ft
- (D) \( H_0: \overline{x} = 32.2 \) ft, \( H_1: \overline{x} > 32.2 \) ft
- (E) \( H_0: \overline{x} = 32.2 \) ft, \( H_1: \overline{x} < 32.2 \) ft
- (F) \( H_0: \overline{x} = 32.2 \) ft, \( H_1: \overline{x} \neq 32.2 \) ft
Choose option (A), testing if the standard deviation is greater than 32.2 ft.
**Test Statistic:**
Calculate the test statistic \(\chi^2 = 36.62\).
**Critical Value:**
Determine the critical value(s):
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