Question 1

Which of the following best describes the concept of 'statistical inference' as covered in the course?

Accepted Answer

Using sample data to make generalizations about a population.

Question 2

A researcher wants to estimate the proportion of students who prefer online classes. She surveys 200 students and finds that 120 prefer online classes. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{120}{200} = 0.60$$

Question 3

Which formula is used to calculate 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 4

A medical study tests whether a new drug lowers blood pressure more than the current standard. Which type of hypothesis test should be used?

Accepted Answer

Two-sample t-test for means

Question 5

If the null hypothesis is $$H_0$$: \mu = 100$$ and the alternative is H_a$$: \mu 
eq 100$$, what type of test is this?

Accepted Answer

Two-tailed test

Question 6

Which of the following is NOT a requirement for using the normal approximation to the binomial distribution?

Accepted Answer

The probability of success must change from trial to trial.

Question 7

A student calculates a $$p-$$value of 0.03 for a hypothesis test with $$\alpha = 0.05. $$What is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 8

Which formula is used to calculate the sample mean $$\bar{x}$$?

Accepted Answer

$$\bar{x} = \frac{\sum x_i}{n}$$

Question 9

A company wants to compare the average salaries of engineers and accountants. Which statistical method should be used?

Accepted Answer

Two-sample t-test for means

Question 10

Which of the following best describes the meaning of a 95% confidence interval for a population mean?

Accepted Answer

We are 95% confident that the interval contains the true population mean.

Question 11

A regression analysis yields the equation $$y = 2x + 5. $$What is the predicted value of $$y$$ when $$x = 4$$?

Accepted Answer

$$y = 2 	imes 4 + 5 = 13$$

Question 12

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

Accepted Answer

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

Question 13

A hospital wants to know if the proportion of patients recovering from a new treatment is different from the national average of 70%. Which hypothesis test should be used?

Accepted Answer

One-sample z-test for proportions

Question 14

Which of the following is a correct interpretation of a $$p-$$value?

Accepted Answer

The probability of observing the sample data, or something more extreme, if the null hypothesis is true.

Question 15

A student rolls a fair six-sided die. What is the probability of rolling a number greater than 4?

Accepted Answer

$$P = \frac{2}{6} = \frac{1}{3}$$

Question 16

Which formula is used to calculate the margin of error for a confidence interval for a population proportion?

Accepted Answer

$$z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

Question 17

A teacher wants to test if the average test score in her class is higher than the school average of 75. Which is the correct null hypothesis?

Accepted Answer

$$H_0$$: \mu = 75$$

Question 18

Which of the following is a real-world example of using regression analysis?

Accepted Answer

Predicting house prices based on square footage and number of bedrooms.

Question 19

A sample of 50 students has a mean score of 80 and a standard deviation of 10. What is the standard error of the mean?

Accepted Answer

$$SE = \frac{10}{\sqrt{50}} \approx 1.41$$

Statistics 1530: Quantitative Literacy and Applied Statistics Study Guide

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