Question

In a test of hypothesis to determine if a population standard deviation on the length of a part was equal to 4 inches (H₀ ) or was less than 4 inches (H₁) _, the test statistic was computed to be 1.69 from a sample of n = 8. Determine the p-value to three decimal places.

In a test of hypothesis to determine if a population mean on the length of a part was equal to 4 inches (H₀ ) or was less than 4 inches (H₁), the test statistic was computed to be 2.998 from a sample of n = 8. The variance was unknown. Determine the p-value to two decimal places.

Answer 1

1) The null and alternative hypotheses would be

                       (left tailed test)

Ho:σ = 4 Ηα:σ<4

where $\sigma$ is the standard deviation on the length of the part

Chi square hypothesis test is used for testing hypothesis test for standard deviation

Given

x2 = 1.69

n = 8, hence degrees of freedom df = n - 1 = 8 - 1 = 7

For finding p-value , we use the Excel function CHISQ.DIST($\chi ^{2}$, df, TRUE)

p-value = CHISQ.DIST(1.69, 7, TRUE)

p-value = 0.025

2) The null and alternative hypotheses would be

                       (left tailed test)

Ho:μ = 4 Ηα:μ<4

where $\mu$ is the standard deviation on the length of the part

t test is used for testing hypothesis test for mean since sample size is small and variance is unknown

Given t = 2.998

n = 8, hence degrees of freedom df = n - 1 = 8 - 1 = 7

For finding p-value , we use the Excel function  t.dist(t, df, TRUE)

p-value =  t.dist(2.998, 7, TRUE)

p-value = 0.99