Q: A researcher collects data on the number of hours per week 30 students spend on social media. If 6 students spend 0–4 hours and 10 students spend 5–9 hours, what percentage of students spend fewer than 10 hours per week on social media?

$$\frac{6+10}{30} \times 100\% = 53.3\%$$

Question 1

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

Accepted Answer

A parameter describes a characteristic of a population, while a statistic describes a characteristic of a sample.

Question 2

A researcher wants to estimate the average cholesterol level of adults in a city. She divides the city into neighborhoods, randomly selects 5 neighborhoods, and surveys every adult in those neighborhoods. Which sampling method is she using?

Accepted Answer

Cluster sampling

Question 3

Which of the following is an example of interval-level data?

Accepted Answer

Temperature in degrees Fahrenheit

Question 4

A data set of exam scores is right-skewed (positively skewed). Which of the following is most likely true?

Accepted Answer

The mean is greater than the median.

Question 5

Given a bell-shaped distribution with mean $$\mu = 100$$ and standard deviation $$\sigma = 15$$, according to the Empirical Rule, approximately what percentage of data falls between $$85$$ and $$115$$?

Accepted Answer

68%

Question 6

A student’s test score is $$x = 62 in a $$class where the mean is $$\bar{x} = 70$$ and the standard deviation is $$s = 4. $$What is the z-score for this student?

Accepted Answer

$$z = -2.0$$

Question 7

A frequency distribution of quiz scores is as follows: 50–59: 2, 60–69: 6, 70–79: 10, 80–89: 7, 90–99: 5. What is the relative frequency for the 70–79 class?

Accepted Answer

$$\frac{10}{30} = 0.333$$

Question 8

Which of the following variables is best classified as qualitative and measured at the nominal level?

Accepted Answer

Types of blood groups (A, B, AB, O)

Question 9

A data set has a mean of $$\bar{x} = 40$$ and a standard deviation of $$s = 8. $$According to Chebyshev’s Theorem, at least what percentage of data values must lie within 2 standard deviations of the mean?

Accepted Answer

75%

Question 10

A sample of 12 students’ weekly study hours (in ascending order) is: 2, 4, 5, 7, 8, 10, 12, 14, 15, 18, 20, 25. What is the interquartile range (IQR)?

Accepted Answer

$$Q_3$$ - $$Q_1 = 15.75 - 5.5 = 10.25$

Question 11

A hospital administrator wants to estimate the average length of stay for patients. She divides patients into age groups (0–18, 19–35, 36–60, 61+), then randomly selects 10 patients from each group. What sampling method is this?

Accepted Answer

Stratified sampling

Question 12

A data set has a mean of $$\bar{x} = 60$$ and a standard deviation of $$s = 10. $$What is the range of values that includes approximately 95% of the data, assuming a bell-shaped distribution?

Accepted Answer

$$40 to$$ $$80$$

Question 13

A student scored at the 80th percentile on a statistics exam. Which of the following best describes what this means?

Accepted Answer

The student scored higher than 80% of the students who took the exam.

Question 14

Given the data set: 3, 5, 7, 8, 10, 12, 14, 15, 18, 28, which measure of center is least affected by the outlier 28?

Accepted Answer

Median

Question 15

A sample of 20 students reported the following hours of sleep: 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 11. What is the mode?

Accepted Answer

7

Question 16

A data set has a mean of $$\bar{x} = 74$$ and a standard deviation of $$s = 9. A $$student scored $$88. $$What is the z-score for this student?

Accepted Answer

$$z = 1.56$$

Question 17

A frequency distribution for body temperatures (in $$^\circF) of 100 $$adults is given. The class 97.0–97.5 has a frequency of 15. What is the midpoint of this class?

Accepted Answer

$$\frac{97.0 + 97.5}{2} = 97.25$$

Question 18

If a data value has a z-score of $$-2.5$$, what does this indicate about the data value?

Accepted Answer

It is 2.5 standard deviations below the mean and is considered unusual.

Question 19

A data set has a mean of $$\bar{x} = 50$$ and a standard deviation of $$s = 5. $$What is the z-score for a data value of $$x = 40$$?

Accepted Answer

$$z = -2.0$$

Question 20

A researcher collects data on the number of hours per week 30 students spend on social media. If 6 students spend 0–4 hours and 10 students spend 5–9 hours, what percentage of students spend fewer than 10 hours per week on social media?

Accepted Answer

$$\frac{6+10}{30} 	imes 100\% = 53.3\%$$

STA 2023 Test 1 Preview – Step-by-Step Statistics Study Guide

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