Q: A scale reads 150.5 lb for a person whose true weight is 148.0 lb. What is the relative error?

$$\frac{150.5 - 148.0}{148.0} \times 100\% = 1.69\%$$

Q: A company’s revenue increased from $$2,000,000 to 2$$,500,000. What is the relative change?

$$\frac{2,500,000 - 2,000,000}{2,000,000} \times 100\% = 25\%$$

Q: A frequency table shows the following counts for number of siblings: 0 (5), 1 (10), 2 (8), 3 (4), 4 (3). What percent of students have 2 or fewer siblings?

$$\frac{5+10+8}{30} \times 100\% = 76.7\%$$

Question 1

A researcher surveys 1,200 randomly selected college students and finds that 55% report eating breakfast daily. Which of the following is the sample statistic?

Accepted Answer

55%

Question 2

A poll reports that 38% of respondents support a new city park, with a margin of error of 4 percentage points. What is the confidence interval for the true percentage of support?

Accepted Answer

$$38\% \pm 4\% = 34$$\%$$ to 42$$\%$

Question 3

A school randomly selects 10 of its 50 classrooms and surveys every student in those rooms. Which sampling method is used?

Accepted Answer

Cluster sampling

Question 4

A researcher divides employees into managers and staff, then randomly selects 20 managers and 20 staff for a survey. What sampling method is this?

Accepted Answer

Stratified sampling

Question 5

Which of the following best describes a systematic error?

Accepted Answer

A consistent error that affects all measurements in the same direction and by a similar amount

Question 6

A thermometer consistently reads 2°C higher than the actual temperature. What is the absolute error if the true temperature is 20°C and the thermometer reads 22°C?

Accepted Answer

$$22 - 20 = 2\ 	ext{°C}$$

Question 7

A scale reads 150.5 lb for a person whose true weight is 148.0 lb. What is the relative error?

Accepted Answer

$$\frac{150.5 - 148.0}{148.0} 	imes 100\% = 1.69\%$$

Question 8

A study finds that a new medication reduces blood pressure by an average of 1 mmHg more than the control group. Which statement best describes the practical significance?

Accepted Answer

The result is statistically significant but may lack practical significance because 1 mmHg is a small effect.

Question 9

Which of the following is an example of quantitative continuous data?

Accepted Answer

The exact height of each student in a class

Question 10

A radio host asks listeners to call in and share their opinion on a new law. 5,000 people call, and 80% oppose it. Why should this result not be trusted?

Accepted Answer

The sample is biased due to voluntary participation; callers are not representative of the population.

Question 11

A company’s revenue increased from $$2,000,000 to 2$$,500,000. What is the relative change?

Accepted Answer

$$\frac{2,500,000 - 2,000,000}{2,000,000} 	imes 100\% = 25\%$$

Question 12

A price is 20% less than $80. What is the new price?

Accepted Answer

$$0.80 	imes 80 = 64$

Question 13

Which graph is most appropriate for displaying the number of customers in each service category: takeout, dine-in, delivery, and catering?

Accepted Answer

Bar graph

Question 14

A frequency table shows the following counts for number of siblings: 0 (5), 1 (10), 2 (8), 3 (4), 4 (3). What percent of students have 2 or fewer siblings?

Accepted Answer

$$\frac{5+10+8}{30} 	imes 100\% = 76.7\%$$

Question 15

Which of the following best distinguishes a histogram from a bar graph?

Accepted Answer

A histogram is for quantitative data and has touching bars; a bar graph is for qualitative data and has separated bars.

Question 16

A graph shows the yearly percentage change in tuition, with the line falling from 10% to 2% but staying above zero. What does this mean?

Accepted Answer

Tuition is increasing each year, but by smaller percentages.

Question 17

Which of the following is a trap when interpreting pictograms in statistics?

Accepted Answer

The artwork may exaggerate differences by using area or volume instead of length.

Question 18

A study reviews past medical records to compare outcomes for patients who received a treatment versus those who did not. What type of study is this?

Accepted Answer

Observational, retrospective

Question 19

A researcher wants to avoid confounding variables in an experiment. Which strategy is most effective?

Accepted Answer

Assign subjects to treatment and control groups at random and use sufficiently large groups.

Introductory Statistics: Unit 1 Study Guide (Statistical Reasoning, Measurement, and Data Visualization)

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