Question 1

A hospital wants to know if the proportion of patients who recover within a week differs between two treatments. They collect data and organize it into a contingency table. What is the primary purpose of using a contingency table in this scenario?

Accepted Answer

To display the relationship between two categorical variables

Question 2

Which formula correctly represents the addition rule for two mutually exclusive events $$A$$ and $$B$$?

Accepted Answer

$$P(A \cup B) = P(A) + P(B)$$

Question 3

A researcher flips a fair coin 100 times. What is the sample space for this random phenomenon?

Accepted Answer

All possible sequences of 100 heads or tails

Question 4

Which of the following correctly expresses the conditional probability of $$A$$ given $$B$$?

Accepted Answer

$$P(A|B) = \frac{P(A \cap B)}{P(B)}$$

Question 5

A pharmaceutical company tests a new drug and finds the sample mean recovery time is 8 days, with a sample standard deviation of 2 days, from a sample of 25 patients. What is the standard error of the mean?

Accepted Answer

$$SE(\bar{x}) = \frac{2}{\sqrt{25}} = 0.4$$

Question 6

Which condition must be met to use the normal approximation for the sampling distribution of a sample proportion?

Accepted Answer

Both $$np \geq 10$$ and $$n(1-p) \geq 10$$

Question 7

A scientist wants to estimate the proportion of defective products in a large shipment. She samples 100 items and finds 12 are defective. What is the 95% confidence interval for the population proportion?

Accepted Answer

$$\hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

Question 8

Which statement best describes the Central Limit Theorem?

Accepted Answer

The sampling distribution of the sample mean approaches normality as sample size increases, regardless of the population distribution

Question 9

A researcher performs a one-sample $$t-$$test for a mean with $$n = 10$$ and finds the sample is fairly symmetric with no clear outliers. Is it appropriate to use the $$t-$$distribution?

Accepted Answer

Yes, the condition is generally met for all $$n$$, including $$n \u003c 15$$

Question 10

Which formula gives the test statistic for a one-sample test for a proportion?

Accepted Answer

$$z = \frac{\hat{p} - p_0$}{\sqrt{\frac{p_0$(1-p_0$)}{n}}}$$

Question 11

In hypothesis testing, what does a Type I error represent?

Accepted Answer

Rejecting the null hypothesis when it is actually true

Question 12

A medical researcher wants to test if a new treatment is more effective than the standard. She sets up $$H_0$$: the new treatment is equally effective, and $$H_A$$: the new treatment is more effective. What type of hypothesis test is this?

Accepted Answer

One-sided alternative hypothesis

Question 13

Which of the following best describes the relationship between sample size and the standard error of the mean?

Accepted Answer

As sample size increases, the standard error decreases

Question 14

A company wants to compare the proportion of defective products between two factories. Which test statistic should they use?

Accepted Answer

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

Question 15

Which of the following is true about p-values in hypothesis testing?

Accepted Answer

A low p-value indicates strong evidence against the null hypothesis

Question 16

A researcher wants to know if two events $$A$$ and $$B$$ are independent. Which condition must be satisfied?

Accepted Answer

$$P(A|B) = P(A)$$

Question 17

Which scenario best illustrates Simpson's paradox?

Accepted Answer

A drug appears more effective in each age group, but less effective overall when age groups are combined

Question 18

Which formula gives the standard deviation of the sampling distribution of a sample proportion?

Accepted Answer

$$SD(\hat{p}) = \sqrt{\frac{p(1-p)}{n}}$$

Question 19

Which of the following increases the power of a hypothesis test?

Accepted Answer

Increasing the sample size

STAT 118: Exam 3 Study Guide (Chapters 3, 12-16)

Guida di studio - Domande di pratica

Study guide - Flashcard