Question

Let X equal the number of pounds of butterfat produced by a Holstein cow during the 305-day milking period following the birth of a calf. We shall test the null hypothesis 22 22 H0 : σ = 140 against the alternative hypothesis H1 : σ > 140 at α = 0.05, based on given data: n = 25, and a sample standard deviation of s = 150.1. What is the type of the test?A) Right-tailedB) Left-tailedC) Two-tailed2. Calculate Observed Test Statistic3. Find the Critical Value of Critical Region of the Test4. Draw Your Conclusion of the Test at α = 0.05A) Fail to Reject H0B) Reject H0

Answer 1

Explanation:

Given that:

`\mathbf{H_o : \sigma = 140} \\ \\\mathbf{H_i : \sigma > 140} \\ \\ \mathbf{ \alpha = 0.05 \ \ \ \ n = 25 \ \ \ \ S = 150}`

1. This type of test is right tailed since the alternative hypothesis is right tailed

2. The Observed test statistic is calculated as follows:

`X^2 = ((n-1)s^2)/(\sigma^2) \\ \\ X^2 = ((25-1)150^2)/(140^2) \\ \\ X^2 = ((24)22500)/(19,600) \\ \\ X^2 =27.55`

3. Critical Value

where ∝ = 0.05 and the test statistic is right tailed ;

By using
`X^2` table

`X^2 _(\alpha/2 , n-1)= 36.415`

4. Conclusion:

∝ = 0.05

where

X² = 36.415

Therefore ; we reject
`\mathbf{H_o}`