A test of hypothesis has the following details: H₀: μ = 8000, Ha: μ 8000, n = 50, σ = 409, α = 0.01, = 8158
Calculate the p-value and state the correct decision for this test.
A) p-value = 0.0032; fail to reject H₀
B) p-value = 0.3863; fail to reject H₀
C) p-value = 0.3483; reject H₀
D) p-value = 0.0032; reject H₀

Question

A test of hypothesis has the following details: H₀: μ = 8000, Ha: μ > 8000, n = 50, σ = 409, α = 0.01,  = 8158
Calculate the p-value and state the correct decision for this test.
A) p-value = 0.0032; fail to reject H₀ 
B) p-value = 0.3863; fail to reject H₀ 
C) p-value = 0.3483; reject H₀ 
D) p-value = 0.0032; reject H₀

Quizplus · Accepted Answer

To calculate the p-value, we first need to find the test statistic which is given by:

t = (x̄ - μ) / (σ / √n) 
where x̄ is the sample mean.

Now, x̄ = 8158, μ = 8000, σ = 409 and n = 50.

t = (8158 - 8000) / (409 / √50) = 3.134

Using a t-distribution table (with degrees of freedom = n-1 = 49), we find the p-value = 0.0032.

Since p-value < α, we reject the null hypothesis H₀ and conclude that there is sufficient evidence to support the alternative hypothesis Ha: μ > 8000.

A Test of Hypothesis Has the Following Details: H₀: μ