Q: Given the regression equation $$ Y = 28.71 + 4.51X_1 + 2.22X_2 $$, where $$ X_1$ is $$years of experience and $$ X_2$ is $$gender (0 = female, 1 = male), what is the predicted salary (in $1000s) for a male employee with 10 years of experience?

$$ Y = 28.71 + 4.51 \times 10 + 2.22 \times 1 = 75.03 $$

Question 1

Given the regression equation $$ Y = 28.71 + 4.51X_1 + 2.22X_2 $$, where $$ X_1$  is $$years of experience and $$ X_2$  is $$gender (0 = female, 1 = male), what is the predicted salary (in $1000s) for a male employee with 10 years of experience?

Accepted Answer

$$ Y = 28.71 + 4.51 	imes 10 + 2.22 	imes 1 = 75.03 $$

Question 2

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 3

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

Accepted Answer

Convenience sampling; non-representative sample bias

Question 4

After recording the annual average rainfall (in millimeters) for the past 100 years, which type of graph is most appropriate to visualize these data?

Accepted Answer

Line Graph

Question 5

A frequency distribution of delivery times (in minutes) for packages is as follows: 10-19: 4, 20-29: 7, 30-39: 12, 40-49: 8, 50-59: 3. What best describes the shape of the distribution?

Accepted Answer

Skewed right

Question 6

You have data on the number of employees in different departments: HR: 12, IT: 20, Sales: 8. How would you synthesize this information into a bar graph?

Accepted Answer

Create bars for HR, IT, and Sales with heights of 12, 20, and 8 respectively.

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

Organize the data in increasing order.

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. Find the mean. Does the result seem reasonable?

Accepted Answer

78.9 bpm; Yes, the result seems reasonable.

Question 13

Given the following weights (in kg) for two years: Year 1: 72, 75, 78, 70, 74, 77, 73, 76; Year 2: 80, 85, 82, 79, 84, 83, 81, 86. How have the weights changed over time?

Accepted Answer

The weights in Year 2 are higher than in Year 1, as indicated by both the mean and median.

Question 14

Use the data: $$4.5, 5, 6.5, 5.5, 6, 5.7, 6.5, 4.5, 5.5, 6, 5.5, 6.5, 7.5, 6 ($$daily screen time in hours for 14 students). Calculate the mean, median, and mode. Which measure may not represent the center, and why?

Accepted Answer

Mean = 5.68 hours, Median = 5.83 hours, Mode = 7.5 hours. Mode may not represent the center because it is far from the mean and median.

Question 15

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

Accepted Answer

6.32 hours

Question 16

In a study of laptop prices, the mean price is $$1200 with a standard deviation of 180. Is a $$laptop priced at $870 unusual? Explain your reasoning.

Accepted Answer

Yes, because $870 is more than 2 standard deviations below the mean

Question 17

The goals scored by the 50 winning teams in a football tournament final are represented in the ogive below. What score represents the 60th percentile, and what interpretation could be drawn from this?

Accepted Answer

The 60th percentile corresponds to 5 goals. This means that 60% of the winning teams in the football tournament final scored 5 goals or fewer, and 40% scored more than 5 goals.

Statistics Fundamentals: Data Collection, Analysis, and Interpretation

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