Question 1

Which of the following best describes a parameter in statistics?

Accepted Answer

A numerical summary of a population

Question 2

A pharmaceutical company wants to estimate the mean time it takes for a new drug to relieve pain. They randomly select 100 patients and record the time it takes for each patient to report pain relief. What type of sampling is this?

Accepted Answer

Simple random sampling

Question 3

Which formula is used to calculate the standard deviation of a sample?

Accepted Answer

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

Question 4

A researcher wants to test whether the mean waiting time at a fast-food restaurant is less than 5 minutes. Which of the following is the correct null hypothesis?

Accepted Answer

$$H_0$$: \mu \geq 5$$

Question 5

Which of the following is a discrete random variable?

Accepted Answer

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

Question 6

A sample of 50 adults is selected from a city where 30% do not own a credit card. What is the mean of the sampling distribution of the sample proportion?

Accepted Answer

$$\mu_{\hat{p}} = 0.30$$

Question 7

Which of the following statements about the Central Limit Theorem is correct?

Accepted Answer

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

Question 8

A manufacturer claims that 15% of its candies are blue. In a sample of 100 candies, 20 are found to be blue. What is the sample proportion?

Accepted Answer

$$\hat{p} = 0.20$$

Question 9

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

Accepted Answer

Rejecting a true null hypothesis

Question 10

A normal distribution has a mean of 100 and a standard deviation of 15. What is the z-score for a value of 130?

Accepted Answer

$$z = \frac{130 - 100}{15} = 2$$

Question 11

Which of the following is the correct formula for the confidence interval for a population mean when the population standard deviation is unknown?

Accepted Answer

$$\bar{x} \pm t \frac{s}{\sqrt{n}}$$

Question 12

A correlation coefficient $$r = -0.85$$ indicates:

Accepted Answer

A strong negative linear relationship

Question 13

A company wants to compare the mean salaries of employees in two different departments. Which statistical test should be used?

Accepted Answer

Two-sample t-test

Question 14

Which of the following is the formula for the expected value $$E(X) of a $$discrete random variable $$X$$?

Accepted Answer

$$E(X) = \sum x_i p(x_i)$$

Question 15

A researcher wants to test if the proportion of left-handed students in a university is different from 10%. Which test is most appropriate?

Accepted Answer

One-proportion z-test

Question 16

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

Accepted Answer

It is the probability of obtaining a result as extreme as the observed, assuming the null hypothesis is true

Question 17

A boxplot is useful for identifying which of the following?

Accepted Answer

The presence of outliers

Question 18

Which formula is used to calculate the sample proportion?

Accepted Answer

$$\hat{p} = \frac{x}{n}$$

Question 19

A study finds that the mean test score for a class is 75 with a standard deviation of 8. What percentage of scores fall within one standard deviation of the mean in a normal distribution?

Accepted Answer

About 68%

Question 20

Which of the following is the correct formula for the margin of error in a confidence interval for a population proportion?

Accepted Answer

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

Comprehensive Study Guide: Introductory Statistics Concepts and Applications

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