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 or items of interest, while a sample is a subset selected from the population.

Question 2

A pharmaceutical company wants to estimate the average recovery time for a new medication. They collect data from 200 randomly selected patients who used the medication. Which statistical concept allows them to use this data to make inferences about all patients who might use the medication?

Accepted Answer

Inferential statistics

Question 3

Which of the following is NOT a measure of central tendency?

Accepted Answer

Standard deviation

Question 4

A researcher collects the following data on the number of books read by students in a month: 2, 3, 3, 4, 5, 7, 8. What is the median number of books read?

Accepted Answer

$$4$$

Question 5

Which of the following statements about the normal distribution is TRUE?

Accepted Answer

The mean, median, and mode are all equal in a normal distribution.

Question 6

Suppose the heights of adult men in a city are normally distributed with a mean of $$70$$ inches and a standard deviation of $$3$$ inches. What is the $$z-$$score for a man who is $$76$$ inches tall?

Accepted Answer

$$z = 2$$

Question 7

A boxplot is most useful for which of the following purposes?

Accepted Answer

Showing the distribution, center, and spread of numerical data, including outliers

Question 8

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 9

A hospital administrator wants to know if a new training program reduces the average patient wait time. She collects data before and after the program and performs a hypothesis test. Which of the following is the correct null hypothesis ($$H_0$$)?

Accepted Answer

$$H_0$$: \mu_{after} = \mu_{before}$$

Question 10

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

Accepted Answer

If we took many samples and built a confidence interval from each, about $$95\% of $$those intervals would contain the true population mean.

Question 11

A study finds a correlation coefficient $$r = 0.85$$ between hours studied and exam scores. Which of the following best describes this relationship?

Accepted Answer

A strong positive linear relationship

Question 12

Which of the following is an example of a categorical variable?

Accepted Answer

Type of car (sedan, SUV, truck)

Question 13

A fair coin is flipped three times. What is the probability of getting exactly two heads?

Accepted Answer

$$\dfrac{3}{8}$$

Question 14

Which of the following is a key assumption for using linear regression to model the relationship between two variables?

Accepted Answer

The relationship between the variables is linear.

Question 15

A researcher wants to estimate the proportion of voters who support a new policy. She surveys a random sample of 400 voters and finds that 220 support the policy. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = 0.55$$

Question 16

Which of the following best describes the purpose of using a scatterplot in statistics?

Accepted Answer

To visualize the relationship between two quantitative variables

Question 17

A company claims that their batteries last an average of $$100$$ hours. A consumer group tests $$36$$ batteries and finds a sample mean of $$98$$ hours with a standard deviation of $$6$$ hours. What is the $$z-$$score for the sample mean?

Accepted Answer

$$z = \dfrac{98 - 100}{6/\sqrt{36}} = -2$$

Question 18

Which of the following is NOT a property of the binomial distribution?

Accepted Answer

The probability of success changes from trial to trial.

Question 19

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

Accepted Answer

Reject the null hypothesis because $$0.03 \u003c 0.05.$$

Statistics I (MATH 1200) Syllabus and Course Structure – Housatonic Community College

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