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? ​, ​, ​, ​, ​, ​, ​, ​, ​, ​, ​,

To test a hypothesis, it means we want to verify or refute a claim. Here, we want to verify or refute whether the new method is better or not.

The new method is better, and the company should not take any action.

The given parameters are:

-- significance level

-- the sample standard deviation

The missing data are:

To solve this question, I will use the p-value method

The claim that the standard deviation is greater than 32.2 means that:

The alternate hypothesis is:

The null hypothesis is:

So, we have:

--- null hypothesis

--- alternate hypothesis

Start by calculate the mean value

Next, calculate the sample standard deviation

This gives:

Approximate

--- to 1 decimal place

Next, calculate the test statistic using:

Calculate the degrees of freedom (df)

So, we calculate the p-value with the following parameters

The p value is

Because the p value is less than the significance level

i.e.

We have to reject the null hypothesis and accept the alternative hypothesis

This means that the new method is better, and the company should not take any action.

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