Question 1

Which of the following best describes the Central Limit Theorem?

Accepted Answer

It states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the population's distribution.

Question 2

A researcher collects data on the heights of 1000 college students. Which measure would best describe the most typical height?

Accepted Answer

The mean

Question 3

Which formula correctly calculates the sample standard deviation $$s$$ for a dataset $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2$}$$

Question 4

A pharmaceutical company wants to estimate the proportion of patients who experience side effects from a new drug. Which statistical method should they use?

Accepted Answer

Construct a confidence interval for the population proportion.

Question 5

Which of the following is NOT a measure of central tendency?

Accepted Answer

Standard deviation

Question 6

Suppose the probability of a defective item in a factory is 0.02. If 50 items are selected at random, which distribution best models the number of defective items?

Accepted Answer

Binomial distribution

Question 7

Given the regression equation $$y = 2 + 3x$$, what is the predicted value of $$y$$ when $$x = 4$$?

Accepted Answer

$$y = 14$$

Question 8

Which of the following statements about hypothesis testing is TRUE?

Accepted Answer

The alternative hypothesis is rejected if the p-value is greater than the significance level.

Question 9

A boxplot is most useful for displaying which of the following?

Accepted Answer

The distribution, spread, and potential outliers of a dataset

Question 10

If the correlation coefficient $$r$$ between two variables is $$-0.85$$, what does this indicate?

Accepted Answer

There is a strong negative linear relationship.

Question 11

Which formula gives the probability of exactly $$k$$ successes in $$n$$ independent Bernoulli trials with probability $$p of $$success?

Accepted Answer

$$P(X = k) = \binom{n}{k} p^k (1-p$$)^{n-k}$$

Question 12

A 95% confidence interval for a population mean is calculated as $$(50, 60). $$Which of the following is a correct interpretation?

Accepted Answer

We are 95% confident that the population mean is between 50 and 60.

Question 13

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

Accepted Answer

Rejecting a true null hypothesis

Question 14

A hospital administrator wants to know if a new training program reduces the average patient wait time. Which statistical test should be used?

Accepted Answer

A hypothesis test for the population mean

Question 15

Which of the following is a limitation of statistical analysis that students should acknowledge?

Accepted Answer

Bias and perspective can affect the interpretation of results.

Introductory Statistics I (MTH 160) Course Syllabus and Study Guide

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