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 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 hte 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?

-40, 78,-24,-70,-40,15,19,54,-9,-51,-106,-106

What are the null and alternative hypotheses?

A. standard deviation =32.2 ft standard deviation greater than 32.2 ft

Answer 1

To test the claim about the new production method's error standard deviation, the null hypothesis states that the standard deviation is equal to 32.2 ft, while the alternative hypothesis claims it is greater. We use the chi-square test for variance to determine if the standard deviation exceeds 32.2 ft, and reject the null hypothesis if our test statistic is significant at the 0.05 level.

Step-by-step explanation:

To test the claim whether the new production method for aircraft altimeters has errors with a standard deviation greater than 32.2 ft, we will use a hypothesis test for variance. Given the significance level of 0.05, the null hypothesis (H_o) and the alternative hypothesis (Ha) can be stated as follows:

• H_o: σ = 32.2 ft (The standard deviation of errors is equal to 32.2 ft)
• Ha: σ > 32.2 ft (The standard deviation of errors is greater than 32.2 ft)

The test statistic for this hypothesis test is based on the chi-square distribution since the sample comes from a normally distributed population. This statistic is calculated using the formula:

Chi-square (X^2) = (n - 1)*s^2 / σ^2

where n is the sample size, s is the sample standard deviation, and σ is the claimed standard deviation of the population. We then compare the calculated test statistic to the critical chi-square value based on the degrees of freedom (n - 1) and the chosen alpha level of 0.05.

If the test statistic exceeds the critical value, or if the p-value is less than 0.05, we reject the null hypothesis, indicating there is sufficient evidence to suggest that the standard deviation is greater than 32.2 ft. This would imply that the new production method is worse than the old method in terms of variability of altimeter errors, and the company should consider taking action.