A simple random sample of 25 vitamin tablets is obtained, and the potassium content of each tablet is measured. The sample has a standard deviation of 3.7 mg. Use a 0.05 significance level to test the claim that the potassium content of vitamin tablets has a standard deviation equal to 3.2 mg. Find the critical value(s) needed to test the claim. Could anyone show me how to do this?

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The standard error is 3.7/√25=3.7/5=0.74mg. We need the critical value for this sample size and significance level of 0.05 (95% confidence level). We use the 2-tailed value because the test is for equality, which means we test for  less than or greater than the claim of 3.2mg. Looking up the critical value in the test table gives us 2.064 (24 degrees of freedom=sample size 25-1).

2.064 times 0.74=1.53 approx for the margin of error: 3.7±1.53 gives us a range of 2.17 to 5.23mg, and 3.2mg lies within this range, so the claim is valid.

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