Q: Which of the following is the correct null and alternative hypothesis for testing if the mean checkout time using the standard method is greater than the Fast Lane method?

$H_0: \mu_{\text{Standard}} \leq \mu_{\text{Fast Lane}},\ H_A: \mu_{\text{Standard}} > \mu_{\text{Fast Lane}}$

Question 1

Which of the following is the correct null and alternative hypothesis for testing if the mean checkout time using the standard method is greater than the Fast Lane method?

Accepted Answer

$H_0: \mu_{	ext{Standard}} \leq \mu_{	ext{Fast Lane}},\ H_A: \mu_{	ext{Standard}} > \mu_{	ext{Fast Lane}}$

Question 2

When comparing two independent population means with known standard deviations, which test statistic formula should be used?

Accepted Answer

$z = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}$

Question 3

A business wants to test if a new training program reduces the average number of customer complaints. They collect 'before' and 'after' data from the same employees. Which hypothesis test is most appropriate?

Accepted Answer

Matched-pair (dependent samples) t-test

Question 4

Which of the following is an assumption for conducting a hypothesis test comparing two independent population means?

Accepted Answer

The two samples are randomly and independently selected from their respective populations.

Question 5

Given $\sigma_1 = 0.40$, $\sigma_2 = 0.30$, $n_1 = 50$, $n_2 = 100$, $\bar{x}_1 = 5.50$, $\bar{x}_2 = 5.30$, calculate the value of the test statistic for $H_0: \mu_1 \leq \mu_2$ at $\alpha = 0.01$.

Accepted Answer

$z = 3.123$

Question 6

If the calculated test statistic is $z = 3.123$ and the critical value at $\alpha = 0.01$ (one-tailed) is $2.33$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is evidence the Fast Lane is faster.

Question 7

Which formula is used to calculate the pooled variance when population standard deviations are unknown but assumed equal?

Accepted Answer

$s_p^2 = \frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}$

Question 8

In a matched-pair test, what is the correct formula for the test statistic?

Accepted Answer

$t = \frac{\bar{d}}{s_d / \sqrt{n}}$

Question 9

A company wants to compare the mean sales of two independent stores. The population standard deviations are unknown but assumed equal. Which distribution should be used to find the critical value?

Accepted Answer

t-distribution with $df = n_1 + n_2 - 2$

Question 10

Which of the following best describes independent samples?

Accepted Answer

Samples where the selection of one sample does not influence the selection of the other.

Question 11

If the sample sizes are both greater than 30, but the population distributions are not normal, what justifies using the normal approximation for the sampling distribution of $\bar{x}_1 - \bar{x}_2$?

Accepted Answer

The Central Limit Theorem

Question 12

A researcher collects before and after cholesterol levels from the same patients to test if a new drug is effective. What is the null hypothesis for the matched-pair test?

Accepted Answer

$H_0: \mu_d = 0$

Question 13

Which scenario requires the use of a two-sample t-test with pooled variance?

Accepted Answer

Comparing the mean test scores of two independent classes with unknown but equal variances.

Question 14

A company wants to know if the mean productivity differs between two departments. Which alternative hypothesis would be used for a two-tailed test?

Accepted Answer

$H_A: \mu_1 
eq \mu_2$

Question 15

In a matched-pair test, the sample mean difference is $\bar{d} = -4.2$, the standard deviation of differences is $s_d = 5.67$, and $n = 5$. What is the value of the test statistic?

Accepted Answer

$t = -1.66$

Question 16

If the calculated t-statistic for a matched-pair test is $-1.66$ and the critical value at $\alpha = 0.01$ (two-tailed, $df = 4$) is $\pm 4.604$, what is the correct decision?

Accepted Answer

Do not reject the null hypothesis.

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