Q: Given the five-number summary: minimum = 10, Q1 = 20, median = 30, Q3 = 40, maximum = 60, what is the interquartile range (IQR)?

$$\text{IQR} = Q_3$ - Q_1$ = 40 - 20 = 20$$

Q: If the probability of event A is $$0.3$$ and the probability of event B is $$0.5$$, and A and B are independent, what is the probability of both A and B occurring?

$$P(A \text{ and } B) = 0.3 \times 0.5 = 0.15$$

Question 1

A medical researcher wants to estimate the proportion of patients who respond positively to a new drug. She randomly selects 100 patients from a hospital and finds that 60 responded positively. Which of the following best describes the population, sample, parameter, and statistic in this study?

Accepted Answer

Population: All patients in the hospital; Sample: 100 selected patients; Parameter: Proportion of all patients who respond positively; Statistic: Proportion of 100 patients who responded positively

Question 2

Which of the following best describes bias in a sampling method?

Accepted Answer

Bias occurs when the sample does not accurately represent the population due to systematic errors in the sampling process.

Question 3

A study investigates the effect of a new fertilizer on plant growth. Plants are randomly assigned to two groups: one receives the new fertilizer, the other does not. Which of the following is the factor of interest?

Accepted Answer

The type of fertilizer used

Question 4

Which of the following is NOT a key component of experimental design?

Accepted Answer

Correlation coefficient

Question 5

A dataset of exam scores is described as skewed right. Which of the following statements is most likely true?

Accepted Answer

The mean is greater than the median.

Question 6

Given the five-number summary: minimum = 10, Q1 = 20, median = 30, Q3 = 40, maximum = 60, what is the interquartile range (IQR)?

Accepted Answer

$$	ext{IQR} = Q_3$ - Q_1$ = 40 - 20 = 20$$

Question 7

If a boxplot shows a data point at 65, and the upper fence is calculated as $$Q_3 + 1.5$$ 	imes 	ext{IQR} = 40 + 1.5 	imes 20 = 70$$, is 65 an outlier?

Accepted Answer

No, because it is below the upper fence.

Question 8

A scatterplot of height and weight shows a positive linear trend. Which of the following best describes the correlation coefficient?

Accepted Answer

The correlation coefficient is close to $$1.$$

Question 9

Given a linear regression equation $$y = 2x + 5$$, what is the estimated slope and y-intercept?

Accepted Answer

Slope: $$2$$, y-intercept: $$5$$

Question 10

If the probability of event A is $$0.3$$ and the probability of event B is $$0.5$$, and A and B are independent, what is the probability of both A and B occurring?

Accepted Answer

$$P(A 	ext{ and } B) = 0.3 	imes 0.5 = 0.15$$

Question 11

A student scores 85 on a test where the mean is 75 and the standard deviation is 5. What is the z-score?

Accepted Answer

$$z = \frac{85 - 75}{5} = 2$$

Question 12

Which formula would you use to calculate the standard error of the difference in proportions between two groups?

Accepted Answer

$$SE = \sqrt{\frac{p_1$(1-p_1$)}{n_1$} + \frac{p_2$(1-p_2$)}{n_2$}}$$

Question 13

A binomial experiment has $$n = 10$$ trials and probability of success $$p = 0.4. $$What is the probability of exactly 3 successes?

Accepted Answer

$$P(X=3) = \binom{10}{3} (0.4)^3$ (0.6)^7$

Question 14

Which of the following is a condition for creating a confidence interval for a population proportion?

Accepted Answer

Both $$np$$ and $$n(1-p)$$ must be at least 10.

Question 15

A researcher wants a margin of error of $$0.03$$ for a 95% confidence interval for a population proportion. If the estimated proportion is $$0.5$$, what sample size is needed? (Use $$z = 1.96)$$

Accepted Answer

$$n = \hat{p}(1-\hat{p}) \left( \frac{z}{E} \$$right)^2$$ = 0.5 	imes 0.5 \left( \frac{1.96}{0.03} \$$right)^2$$ \approx 1067$$

Question 16

Which of the following best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting a true null hypothesis.

Question 17

A two-sample t-test is used to compare the mean blood pressure between two independent groups. Which formula is used to calculate the standard error of the difference in means?

Accepted Answer

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

Question 18

Which of the following is an assumption for a one-sample t confidence interval for population mean?

Accepted Answer

The sample must be randomly selected and the population must be approximately normal if $$n \u003c 30.$$

Question 19

A researcher collects paired data from the same subjects before and after a treatment. Which test should be used to compare the means?

Accepted Answer

Two-sample t-test for dependent means

Comprehensive Study Guide for Introductory Statistics Final Exam

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