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
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.