Question

A sample of 40 observations is selected from one population with a population standard deviation of 5. The sample mean is 102. A sample of 50 observations is selected from a second population with a population standard deviation of 6. The sample mean is 99. Conduct the following test of hypothesis using the .04 significance level.
Is this a one-tailed or a two-tailed test?

State the decision rule.

Compute the value of the test statistic.

What is your decision regarding H0?

What is the p-value?

Answer 1

1) This is a Two tailed Test.

2) Decision rule is; If the p-value is greater than 4% fail to reject H₀.

3) P-value = 0.00968764 and so we reject H₀

How to state the decision rule in hypothesis testing?

We are given the hypothesis as;

Null Hypothesis; H₀: m₁ = m₂

Alternative Hypothesis; H₁: m₁ ≠ m₂

1) Since the alternative hypothesis has "not equal to sign", then it is a two tailed test.

2) Since we are told to use significance level as 0.04, then we can say that the decision rule is;

If the p-value is greater than 4% fail to reject H₀.

3) Using a 2-Sample Z-Test online TI calculator gives the test statistic as;

z = 2.5868

4) From z-score calculator, p-value equals 0.00968764. This is less than 0.04 and as such the decision regarding H₀ is to reject H₀.

5) P-value = 0.00968764

Read more about decision rule in Hypothesis Testing at; brainly.com/question/17192140

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