I said building up sample of 25 vitamin tablets is obtained in the potassium contact of each tablet is measured. The sample has a standard deviation of 3.7 mg. Is 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 needed to

Answer 1

perform the hypothesis test.

To test the claim that the standard deviation of the potassium content of vitamin tablets is equal to 3.2 mg, we will use a chi-square test.

The null hypothesis is H0: σ = 3.2 mg
The alternative hypothesis is H1: σ ≠ 3.2 mg

Since we are working with a sample size of 25 tablets, we will use a chi-square distribution with n-1 degrees of freedom, where n is the sample size.

Degrees of freedom = n - 1 = 25 - 1 = 24

To find the critical value, we will look up the chi-square value for a 95% confidence level and 24 degrees of freedom. Using a chi-square table or calculator, we find that the critical values are 12.401 and 39.364.

Therefore, the critical values needed to perform the hypothesis test are 12.401 and 39.364.