Q: Given the dataset on employee salaries, gender (0 = female, 1 = male), and years of experience, the multiple regression equation is $$Y = 29.17 + 4.17X_1 + 3.33X_2$$, where $$X_1 is $$years of experience and $$X_2 is $$gender. What is the predicted salary (in $1000s) for a male employee with 10 years of experience?

$$Y = 29.17 + 4.17 \times 10 + 3.33 \times 1 = 73.2$$

Question 1

Given the dataset on employee salaries, gender (0 = female, 1 = male), and years of experience, the multiple regression equation is $$Y = 29.17 + 4.17X_1 + 3.33X_2$$, where $$X_1 is $$years of experience and $$X_2 is $$gender. What is the predicted salary (in $1000s) for a male employee with 10 years of experience?

Accepted Answer

$$Y = 29.17 + 4.17 	imes 10 + 3.33 	imes 1 = 73.2$$

Question 2

Based on the regression equation $$Y = 29.17 + 4.17X_1 + 3.33X_2$$, does gender have a significant effect on salary?

Accepted Answer

Yes, because the coefficient for gender ($$X_2) is $$not zero.

Question 3

Which of the following best describes a census in the context of data collection?

Accepted Answer

A census collects data from every individual in the population.

Question 4

A student stands outside the cafeteria at lunchtime and interviews 40 students who are leaving. What sampling technique is used, and what is a potential source of bias?

Accepted Answer

Convenience sampling; non-representative sample bias.

Question 5

You have recorded the annual average rainfall (in millimeters) for the past 100 years. Which type of graph is most appropriate to visualize this data?

Accepted Answer

Line Graph

Question 6

Given the frequency distribution of delivery times, which histogram best represents the data?

Accepted Answer

The histogram with the highest bar at 30-39 minutes, moderate bars at 20-29 and 40-49, and lower bars at 10-19 and 50-59 minutes.

Question 7

If two pie charts show different percentages for the same category, what can be inferred?

Accepted Answer

The category's representation varies between the two datasets.

Question 8

If a frequency polygon has class midpoints labeled as 20, 40, 60, and 80, what does a point at $$x=60$$ and $$y=20$$ represent?

Accepted Answer

The class with midpoint 60 has a frequency of 20.

Question 9

Given the dataset [1, 2, 2, 4, 4, 4, 5], how many dots will be stacked above the number 4 in the dot plot?

Accepted Answer

Three dots

Question 10

What is the first step in constructing a stemplot from a dataset?

Accepted Answer

Identify stems and leaves.

Question 11

Why do we connect plotted points with segments in a time series graph?

Accepted Answer

To visualize trends in the data.

Question 12

The following are the resting heart rates (in bpm) of adult males: 72, 78, 85, 80, 76, 79, 77, 82, 81. What is the mean heart rate?

Accepted Answer

78.9 bpm

Question 13

A city council is analyzing water usage fees in four neighborhoods. The boxplot shows North has a higher median and greater spread than the others. What can you conclude?

Accepted Answer

Yes, North has the highest median.

Question 14

The number of hours five employees worked in a week is: 32, 36, 40, 44, 48. What is the sample standard deviation? Use $$s = \sqrt{\frac{\sum x^2$ - (\sum x)^2$ / n}{n-1}}.$$

Accepted Answer

6.32 hours

Question 15

In a study of laptop prices, the mean price is $$1,200 with a standard deviation of 180. $$The prices follow a bell-shaped distribution. Is a laptop priced at $870 unusual?

Accepted Answer

No, because $$870 is $$within $$2$$ standard deviations of the mean.

Question 16

The ogive below shows the percentiles for goals scored in a football tournament final. What score represents the 60th percentile, and what does this mean?

Accepted Answer

The 60th percentile corresponds to 4 goals. This means that 60% of the winning teams scored 4 goals or fewer, and 40% scored more than 4 goals.

Step-by-Step Study Guidance for Statistics Midterm (Part 1)

스터디 가이드 - 연습 문제

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