Question 1

Which of the following is the correct formula for the standard error of the difference between two independent sample means when the population standard deviations are known?

Accepted Answer

$$\sqrt{\frac{\$$sigma_1$$^2}{n_1$} + \frac{\$$sigma_2$$^2}{n_2$}}$$

Question 2

A business analyst wants to test if the average customer spending differs between two stores. The population standard deviations are known. Which test statistic should be used?

Accepted Answer

Z-test for the difference between two means

Question 3

Given the following hypotheses for a right-tailed test: $$H_0$$: \$$mu_1$$ - \$$mu_2$$ \leq 0$$, H_1$: \mu_1$ - \mu_2$ \u003e 0$$, and a calculated $$z-$$statistic of 2.3 with a critical value $$z_{\alpha} = 2.05$$, what is the correct conclusion at $$\alpha = 0.02$$?

Accepted Answer

Reject $$H_0$$; there is evidence that $$\mu_1$ \u003e \mu_2$

Question 4

When comparing two population means with independent samples and unknown but equal variances, which formula is used for the pooled variance?

Accepted Answer

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

Question 5

A researcher wants to test if the proportion of customers using online banking is higher among younger customers than older customers. Which is the correct null and alternative hypothesis for this scenario?

Accepted Answer

$$H_0$$: $$p_1$$ - $$p_2$$ \leq 0$$, H_1$: p_1$ - p_2$ \u003e 0$$

Question 6

Which of the following is a necessary assumption when performing a two-sample t-test with independent samples and unknown but equal variances?

Accepted Answer

Both populations are normally distributed or both sample sizes are at least 30

Question 7

If a 95% confidence interval for $$\mu_1$ - \mu_2$ is (2.1, 7.4), what can you conclude about the difference between the two population means?

Accepted Answer

There is evidence that $$\mu_1$ \u003e \mu_2$

Question 8

Which formula is used to calculate the test statistic for comparing two population proportions?

Accepted Answer

$$z = \frac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1-\hat{p})\left(\frac{1}{n_1$} + \frac{1}{n_2$}\right)}}$$

Question 9

A two-tailed hypothesis test is performed at $$\alpha = 0.05$$ with a calculated $$z-$$statistic of $$-2.28. $$The critical values are $$\pm 1.96. $$What is the correct conclusion?

Accepted Answer

Reject $$H_0$$; there is evidence of a difference

Question 10

In a hypothesis test comparing two means with independent samples and unknown, unequal variances, which distribution is used to determine the critical value?

Accepted Answer

Student's t-distribution with degrees of freedom calculated using the Welch-Satterthwaite equation

Question 11

A company wants to know if the average time to pass through security is higher in Philadelphia than in Orlando. The sample means are 14.6 and 11.5 minutes, sample standard deviations are 5.8 and 4.9, and sample sizes are 25 and 27, respectively. Assuming equal variances, which is the correct null hypothesis?

Accepted Answer

$$H_0$$: \$$mu_1$$ - \$$mu_2$$ \leq 0$$

Question 12

Which of the following best describes a Type I error in the context of hypothesis testing for two population means?

Accepted Answer

Rejecting the null hypothesis when it is actually true

Question 13

If the p-value for a hypothesis test is 0.022 and the significance level is 0.05, what is the correct decision?

Accepted Answer

Reject the null hypothesis

Question 14

Which of the following is NOT an assumption for the two-sample z-test for means with known variances?

Accepted Answer

The two samples must be dependent

Question 15

A confidence interval for the difference in proportions between two groups is (-0.05, 0.12). What does this interval suggest?

Accepted Answer

There is no significant difference between the two proportions

Question 16

Which of the following scenarios requires the use of a paired (dependent samples) t-test?

Accepted Answer

Comparing the mean blood pressure of patients before and after taking medication

Chapter 10

Guida di studio - Domande di pratica

Study guide - Flashcard