Q: A hospital administrator wants to estimate the average wait time in the emergency room. She randomly selects 40 patients and finds a sample mean wait time of 2.5 hours with a sample standard deviation of 0.5 hours. What is the 95% confidence interval for the mean wait time? (Use $$t^* = 2.022$$ for 39 degrees of freedom.)

$$ 2.5 \pm 2.022 \times \frac{0.5}{\sqrt{40}} $$

Question 1

Which of the following best describes the difference between a population and a sample in statistics?

Accepted Answer

A population includes all individuals of interest, while a sample is a subset of the population.

Question 2

A pharmaceutical company wants to estimate the average recovery time for a new drug. They select 100 patients from all patients who used the drug. What is the sample in this scenario?

Accepted Answer

The 100 patients selected for the study.

Question 3

Which of the following is a parameter?

Accepted Answer

The average income of all households in a city.

Question 4

Which formula correctly calculates the sample mean $$\bar{x}$$ for a data set with $$n$$ values $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

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

Question 5

A researcher wants to summarize the distribution of exam scores for a class of 200 students. Which graphical method is most appropriate?

Accepted Answer

Histogram

Question 6

Which of the following statements about probability is correct?

Accepted Answer

The probability of a certain event is 1.

Question 7

If a fair six-sided die is rolled, what is the probability of rolling a number greater than 4?

Accepted Answer

$$ \frac{1}{3} $$

Question 8

Which formula is used to calculate the standard deviation $$s of a $$sample with $$n$$ values $$x_1$$, $$x_2$$, ..., x_n$$ and sample mean $$\bar{x}$$?

Accepted Answer

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

Question 9

A normal distribution is characterized by which two parameters?

Accepted Answer

Mean and standard deviation

Question 10

A hospital administrator wants to estimate the average wait time in the emergency room. She randomly selects 40 patients and finds a sample mean wait time of 2.5 hours with a sample standard deviation of 0.5 hours. What is the 95% confidence interval for the mean wait time? (Use $$t^* = 2.022$$ for 39 degrees of freedom.)

Accepted Answer

$$ 2.5 \pm 2.022 	imes \frac{0.5}{\sqrt{40}} $$

Question 11

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 12

A company claims that at least 80% of its products pass quality control. A random sample of 100 products shows that 75 passed. Which hypothesis test is appropriate to evaluate the company's claim?

Accepted Answer

A one-sample z-test for proportions

Question 13

Which of the following is an example of a discrete random variable?

Accepted Answer

The number of cars passing through a toll booth in an hour

Question 14

If $$P(A) = 0.4$$ and $$P(B) = 0.5$$ and $$A$$ and $$B$$ are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$ 0.4 	imes 0.5 = 0.2 $$

Question 15

Which of the following is NOT an assumption for conducting a one-sample t-test?

Accepted Answer

The population standard deviation is known.

Question 16

A researcher wants to compare the mean cholesterol levels between two independent groups. Which statistical test should be used?

Accepted Answer

Two-sample t-test

Question 17

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

Accepted Answer

Rejecting a true null hypothesis

Question 18

A survey asks respondents to select their favorite fruit from a list. What type of data is collected?

Accepted Answer

Qualitative (categorical)

Question 19

Which formula is used to calculate the probability of exactly $$k$$ successes in $$n$$ independent Bernoulli trials with probability $$p of $$success?

Accepted Answer

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

Syllabus Summary: Statistical Reasoning for College Students

Study Guide - Practice Questions

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