## Related questions with answers

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.a. Is this a one-tailed or a two-tailed test? b. State the decision rule. c. Compute the value of the test statistic. d. What is your decision regarding ? e. What is the p-value?

$H_0:μ_1=μ_2; H_1:μ_1≠μ_2$

Solution

VerifiedGiven:

$\begin{align*} H_0&:\mu_1=\mu_2 \\ H_1&:\mu_1\neq \mu_2 \\ n_1&=\text{Sample size}=40 \\ n_2&=\text{Sample size}=50 \\ \overline{x}_1=&\text{Sample mean}=102 \\ \overline{x}_2=&\text{Sample mean}=99 \\ \sigma_1&=\text{Population standard deviation}=5 \\ \sigma_2&=\text{Population standard deviation}=6 \\ \alpha&=\text{Significance level}=0.04 \end{align*}$

(a) If the alternative hypothesis $H_a$ contains $<$, then the test is left-tailed (one-tailed).

If the alternative hypothesis $H_a$ contains $>$, then the test is right-tailed (one-tailed).

If the alternative hypothesis $H_a$ contains $\neq$, then the test is two-tailed.

Two-tailed test

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