Question 1

A researcher surveys 1,000 high school students in grades 9 to 12 from a single city to estimate the average number of hours spent on homework per week. Which of the following best describes the sample and the population in this scenario?

Accepted Answer

The sample is the 1,000 students surveyed; the population is all high school students in grades 9 to 12 in the city.

Question 2

Which of the following variables is quantitative and discrete?

Accepted Answer

The number of books a student owns.

Question 3

A company wants to estimate customer satisfaction. They randomly select 50 customers from their database and survey them. What type of sampling is this?

Accepted Answer

Simple random sampling

Question 4

A medical researcher wants to study the effect of a new drug on blood pressure. She randomly assigns 100 patients to receive the drug and 100 patients to receive a placebo, then compares the results. What type of study is this?

Accepted Answer

Designed experiment

Question 5

A frequency distribution of the number of hours students study per week is given as follows: 0-4 hours: 5 students, 5-9 hours: 12 students, 10-14 hours: 8 students, 15-19 hours: 5 students. What is the relative frequency of the 10-14 hour class?

Accepted Answer

$$ \frac{8}{30} $$

Question 6

A histogram of exam scores is skewed left. Which measure of central tendency is most likely to be greater than the others?

Accepted Answer

The mode

Question 7

A researcher collects data on the number of siblings for each student in a class: 0, 1, 2, 2, 3, 1, 0, 4, 2, 1. What is the mode of this data set?

Accepted Answer

2

Question 8

A relative frequency histogram is constructed for the following data: 10-19: 0.10, 20-29: 0.20, 30-39: 0.30, 40-49: 0.40. What percentage of data falls in the 30-39 class?

Accepted Answer

$$ 30\% $$

Question 9

A pollster wants to estimate the proportion of voters who support a new policy. She divides the city into 10 districts and randomly selects 2 districts, then surveys all voters in those districts. What type of sampling is this?

Accepted Answer

Cluster sampling

Question 10

A data set has a mean of $$ 50 $$ and a standard deviation of $$ 5 . $$According to the Empirical Rule, approximately what percentage of data falls between $$ 45 $$ and $$ 55 $$?

Accepted Answer

$$ 68\% $$

Question 11

A boxplot shows that the median is closer to the lower quartile than the upper quartile, and the upper whisker is much longer than the lower whisker. What can you conclude about the distribution?

Accepted Answer

The distribution is skewed right.

Question 12

A researcher wants to study the relationship between exercise habits and cholesterol levels. She collects data from 200 adults and records their weekly exercise hours and cholesterol levels. What is the explanatory variable?

Accepted Answer

Weekly exercise hours

Question 13

Which of the following best describes the standard deviation?

Accepted Answer

It is the square root of the variance.

Question 14

A study finds that the mean weight of a sample of 50 apples is $$ 150 $$ grams with a standard deviation of $$ 10 $$ grams. What is the z-score for an apple weighing $$ 170 $$ grams?

Accepted Answer

$$ z = 2 $$

Question 15

A relative frequency distribution is constructed for the days of the week that customers visit a store. If the relative frequency for Saturday is $$ 0.25 $$, what does this mean?

Accepted Answer

25% of customers visit on Saturday.

Question 16

A researcher wants to reduce sampling bias in a survey of household income in a city. Which of the following methods is most likely to reduce bias?

Accepted Answer

Randomly select households from all neighborhoods.

Question 17

A data set has the following five-number summary: $$ 	ext{Min} = 10 $$, $$ Q_1$ = 20 $$, $$ 	ext{Median} = 30 $$, $$ Q_3$ = 40 $$, $$ 	ext{Max} = 100 . $$Which of the following statements is true?

Accepted Answer

The data is skewed right.

Question 18

A study reports that the mean height of female university graduates is $$ 165  cm $$with a standard deviation of $$ 6  cm. $$According to the Empirical Rule, what percentage of female graduates are expected to have heights between $$ 159  cm $$and $$ 171  cm$$?

Accepted Answer

$$ 68\% $$

Question 19

A researcher wants to compare the mean test scores of students in two different schools. Which statistical method is most appropriate?

Accepted Answer

Two-sample t-test

Question 20

Which of the following statements about quartiles is correct?

Accepted Answer

Quartiles divide data into fourths.

Fundamentals of Statistics: Data Types, Sampling, Frequency Distributions, and Measures of Central Tendency

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