Question 1

What is the definition of a p-value in hypothesis testing?

Accepted Answer

The probability of finding the observed, or more extreme, data when the null hypothesis is true.

Question 2

A pharmacy wants to test if the mean number of items dispensed per day has increased beyond a target of 165. A sample of 35 days gives a mean of 172.6 and a standard deviation of 16.2. What is the correct formula for the z-test statistic in this scenario?

Accepted Answer

$$z = \frac{\bar{X} - \mu}{\frac{s}{\sqrt{n}}}$$

Question 3

In a two-tailed hypothesis test with a significance level of 0.05, what are the critical z-values for the rejection regions?

Accepted Answer

$$-1.96$$ and $$1.96$$

Question 4

If the p-value for a test statistic is 0.0056, what is the correct decision at a significance level of 0.05?

Accepted Answer

Reject the null hypothesis.

Question 5

Which of the following best describes an independent samples z-test?

Accepted Answer

A hypothesis test used to compare the means of two independent groups.

Question 6

A business collects customer ratings for two products. Product A: mean = 6.7, sd = 2.3, n = 38. Product B: mean = 7.8, sd = 1.4, n = 36. What is the correct formula for the z-test statistic for the difference in means?

Accepted Answer

$$z = \frac{\bar{x}_1 - \bar{x}_2 - (\mu_1$ - \mu_2$)}{\sqrt{\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}}}$$

Question 7

In the context of A/B testing, what is the primary purpose of randomly assigning users to groups?

Accepted Answer

To ensure that any observed differences are due to the intervention and not confounding variables.

Question 8

Which scenario best illustrates paired data?

Accepted Answer

Fitness scores measured before and after a training intervention for the same group of people.

Question 9

A scientist at CERN announces the existence of a particle with a p-value less than 0.000001. What does this imply?

Accepted Answer

There is less than a 1 in a million chance of observing the data if the null hypothesis is true.

Question 10

What is the interpretation of a 95% confidence interval for the difference in population mean ratings between two products?

Accepted Answer

It estimates the range in which the true difference in mean ratings lies with 95% confidence.

Question 11

In an A/B test for an online store promotion, Group A receives a new email and Group B receives the current email. Spending is recorded for both groups. Which statistical test should be used to determine if the new email improved sales?

Accepted Answer

Independent samples z-test

Question 12

If the test statistic for the difference in means is $$z = -2.5$$, and the critical values are $$-1.96$$ and $$1.96$$, what is the correct decision?

Accepted Answer

Reject the null hypothesis.

Question 13

Which of the following is NOT a plausible reason for using a two-tailed test?

Accepted Answer

To test if the mean is exactly equal to a target value.

Question 14

What is the correct formula for a 95% confidence interval for the difference in population means?

Accepted Answer

$$\bar{x}_1 - \bar{x}_2 \pm 1.96 \sqrt{\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}}$$

Question 15

Which of the following statements about p-values is FALSE?

Accepted Answer

A p-value greater than 0.05 means the null hypothesis is definitely true.

Question 16

In hypothesis testing, what does the rejection region represent?

Accepted Answer

The range of values for the test statistic where the null hypothesis is rejected.

Question 17

A company wants to compare two products using customer ratings. Which null hypothesis is appropriate for an independent samples z-test?

Accepted Answer

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

Question 18

Which of the following best describes the standard error for the difference in means between two independent groups?

Accepted Answer

$$\sqrt{\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}}$$

Question 19

In an A/B test, Group A has a mean spending of 147.8, sd = 10.4, n = 100; Group B has a mean of 126.7, sd = 6.3, n = 100. What is the correct formula for the z-test statistic?

Accepted Answer

$$z = \frac{147.8 - 126.7}{\sqrt{\frac{10.4^2$}{100} + \frac{6.3^2$}{100}}}$$

P-values, Independent Samples Tests, and A/B Testing in Statistics

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