Q: A hospital administrator wants to estimate the average wait time in the emergency room. She collects a random sample of 50 wait times and calculates a sample mean of 38 minutes with a standard deviation of 8 minutes. What is the 95% confidence interval for the mean wait time? (Use $z^* = 1.96$)

$38 \pm 1.96 \times \frac{8}{\sqrt{50}}$

Question 1

Which of the following best describes the difference between an observational study and a designed experiment in statistics?

Accepted Answer

An observational study observes outcomes without intervention, while a designed experiment involves actively manipulating variables to observe effects.

Question 2

A pharmaceutical company wants to test a new drug. They randomly assign 100 patients to receive the drug and 100 to receive a placebo, then compare recovery rates. Which type of sampling and study design is this?

Accepted Answer

Simple random sampling and designed experiment

Question 3

Which of the following is the correct formula for the sample mean $\bar{x}$ of a data set with $n$ observations $x_1, x_2, ..., x_n$?

Accepted Answer

$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$

Question 4

A researcher collects the following data on the number of hours students study per week: 5, 7, 8, 10, 10, 12, 15. What is the median?

Accepted Answer

10

Question 5

Which of the following best describes the purpose of a confidence interval in statistics?

Accepted Answer

To provide a range of plausible values for a population parameter based on sample data

Question 6

Suppose the heights of adult males are normally distributed with mean $\mu = 70$ inches and standard deviation $\sigma = 3$ inches. What is the $z$-score for a man who is 76 inches tall?

Accepted Answer

$z = \frac{76 - 70}{3} = 2$

Question 7

Which of the following is NOT an assumption for performing a one-sample $t$-test for a population mean?

Accepted Answer

The population standard deviation is known.

Question 8

A hospital administrator wants to estimate the average wait time in the emergency room. She collects a random sample of 50 wait times and calculates a sample mean of 38 minutes with a standard deviation of 8 minutes. What is the 95% confidence interval for the mean wait time? (Use $z^* = 1.96$)

Accepted Answer

$38 \pm 1.96 	imes \frac{8}{\sqrt{50}}$

Question 9

Which of the following best describes the Central Limit Theorem?

Accepted Answer

The distribution of sample means approaches a normal distribution as the sample size increases, regardless of the population's distribution.

Question 10

A researcher wants to test if a new teaching method improves test scores. She randomly assigns students to two groups: one uses the new method, the other the traditional method. Which statistical test should she use to compare the means of the two groups?

Accepted Answer

Two-sample $t$-test for independent samples

Question 11

Which of the following is the correct formula for the variance $s^2$ of a sample with $n$ observations $x_1, x_2, ..., x_n$ and sample mean $\bar{x}$?

Accepted Answer

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

Question 12

A company wants to know if the proportion of defective products differs between two factories. Which hypothesis test should be used?

Accepted Answer

Two-sample $z$-test for proportions

Question 13

Which of the following is a characteristic of a normal distribution?

Accepted Answer

It is symmetric and bell-shaped.

Question 14

A researcher calculates a $p$-value of 0.03 in a hypothesis test with significance level $\alpha = 0.05$. What is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 15

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter describes a population, while a statistic describes a sample.

Question 16

A regression analysis yields the equation $\hat{y} = 2 + 3x$. What is the predicted value of $y$ when $x = 4$?

Accepted Answer

$\hat{y} = 2 + 3 	imes 4 = 14$

Question 17

Which of the following is the correct formula for the standard error of the mean for a sample of size $n$ with standard deviation $s$?

Accepted Answer

$SE = \frac{s}{\sqrt{n}}$

Question 18

A survey asks 1000 randomly selected adults if they support a new law. 620 say yes. What is the sample proportion $\hat{p}$?

Accepted Answer

$\hat{p} = \frac{620}{1000} = 0.62$

Question 19

Which of the following is a potential consequence of using non-random sampling in a study?

Accepted Answer

The results may not be generalizable to the population.

Statistics Course Syllabus and Topical Outline – Kankakee Community College (MATH 1774)

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