Question 1

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

Accepted Answer

A statistic is a numerical characteristic of a sample, while a parameter is a numerical characteristic of a population.

Question 2

Suppose the heights (in cm) of five randomly selected students are: 160, 165, 170, 175, and 180. What is the sample variance $$s^2 of $$these heights?

Accepted Answer

$$s^2 = 62.5$

Question 3

In simple linear regression, what are the names typically given to the variables $$X$$ and $$Y$$?

Accepted Answer

$$X = $$Predictor variable, $$Y = $$Response variable

Question 4

A researcher finds the regression equation $$\hat{y} = 2 + 3x. $$What is the correct interpretation of the slope in this context?

Accepted Answer

For every one unit increase in $$x$$, $$y$$ increases by 3 units.

Question 5

If the coefficient of determination $$R^2 = 0.64$ in a regression analysis predicting exam scores from hours studied, what does this mean?

Accepted Answer

64% of the variability in exam scores is explained by hours studied.

Question 6

Which of the following is NOT a characteristic of a binomial random variable?

Accepted Answer

There are more than two possible outcomes per trial.

Question 7

A pharmaceutical company wants to estimate the proportion of patients who experience side effects from a new drug. They collect a random sample of 200 patients and find that 30 experienced side effects. Construct a 95% confidence interval for the population proportion $$p. $$Which formula should be used?

Accepted Answer

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

Question 8

Which of the following best defines a simple random sample?

Accepted Answer

A sample where each element in the population has an equally likely chance of being selected.

Question 9

A random variable is best described as:

Accepted Answer

A variable that assumes a numerical value for each outcome of an experiment.

Question 10

A hospital administrator wants to compare the average recovery times for two different treatments. Which formula should be used to construct a confidence interval for the difference in two population means?

Accepted Answer

$$(\bar{x}_1 - \bar{x}_2) \pm t^* \sqrt{\dfrac{s_1$^2}{n_1$} + \dfrac{s_2$^2}{n_2$}}$$

Question 11

A researcher wants to test if the average commute time in a city is different from 30 minutes. Which of the following is the correct null hypothesis ($$H_0$$)?

Accepted Answer

$$H_0$$: \mu = 30$$

Question 12

Which of the following steps is NOT part of the five-step hypothesis testing procedure?

Accepted Answer

Calculate the population parameter.

Question 13

A company claims that at least 90% of its products pass quality control. In a random sample of 100 products, 85 pass. What is the alternative hypothesis ($$H_a) $$for testing if the true proportion is less than 90%?

Accepted Answer

$$H_a: p \u003c 0.90$$

Question 14

A sample of 25 patients has a mean cholesterol level of 200 mg/dL with a standard deviation of 20 mg/dL. Construct a 95% confidence interval for the population mean. Which formula should be used?

Accepted Answer

$$\bar{x} \pm t^* \dfrac{s}{\sqrt{n}}$$

Question 15

Which of the following statements about the sample variance is correct?

Accepted Answer

The sample variance measures the average squared distance of the observations from the mean.

Question 16

A hypothesis test for two population means yields a p-value of 0.03. If the significance level $$\alpha = 0.05$$, what is the correct statistical decision?

Accepted Answer

Reject $$H_0$$ because the p-value is less than $$\alpha.$$

Question 17

Which of the following is a correct interpretation of a 95% confidence interval for a population mean?

Accepted Answer

We are 95% confident that the population mean lies within the interval.

Question 18

A fair coin is flipped 10 times. Which of the following best describes this experiment?

Accepted Answer

It is a binomial experiment because each flip is independent, there are two outcomes, and the probability of heads remains constant.

Question 19

A study finds a correlation coefficient $$r = -0.85$$ between hours of TV watched per week and GPA among college students. What does this indicate?

Accepted Answer

There is a strong negative linear relationship between hours of TV watched and GPA.

Statistics Final Exam Review: Key Concepts and Methods

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