Q: A professor calculates the weighted mean of grades where homework counts for 40% and exams for 60%. If a student scores 80 on homework and 90 on exams, what is the weighted mean?

$$ (0.4 \times 80) + (0.6 \times 90) = 32 + 54 = 86 $$

Question 1

Which of the following best describes the difference between inferential and descriptive statistics?

Accepted Answer

Descriptive statistics summarize and organize data, while inferential statistics use sample data to make generalizations about a population.

Question 2

A researcher wants to compare the heights of students in two different classes. Which scale of measurement is most appropriate for this variable?

Accepted Answer

Ratio

Question 3

Which of the following is an example of a continuous variable?

Accepted Answer

Temperature measured in degrees Celsius

Question 4

Given the following frequency distribution for exam scores: 60-69 (5 students), 70-79 (8 students), 80-89 (12 students), 90-99 (5 students), what is the relative frequency for the 80-89 interval?

Accepted Answer

$$ \frac{12}{30} = 0.40 $$

Question 5

Which graph is most appropriate for displaying the frequency distribution of a continuous variable such as reaction time?

Accepted Answer

Histogram

Question 6

Calculate the mean for the following sample data set: 4, 8, 6, 10, 2.

Accepted Answer

$$ \frac{4+8+6+10+2}{5} = 6 $$

Question 7

A professor calculates the weighted mean of grades where homework counts for 40% and exams for 60%. If a student scores 80 on homework and 90 on exams, what is the weighted mean?

Accepted Answer

$$ (0.4 	imes 80) + (0.6 	imes 90) = 32 + 54 = 86 $$

Question 8

What is the median of the following data set: 3, 7, 9, 12, 15, 18?

Accepted Answer

$$ \frac{9+12}{2} = 10.5 $$

Question 9

Which measure of variability is least affected by extreme scores in a data set?

Accepted Answer

Interquartile range

Question 10

Given the data set: 2, 4, 4, 6, 8, what is the variance?

Accepted Answer

$$ \frac{(2-4.8)^2$ + (4-4.8)^2$ + (4-4.8)^2$ + (6-4.8)^2$ + (8-4.8)^2$}{5} = 4.16 $$

Question 11

A psychologist finds that the standard deviation of reaction times in a sample is $$ 0.25 $$ seconds. What does this value represent?

Accepted Answer

The average distance of reaction times from the mean

Question 12

If the probability of a patient recovering from a disease is $$ 0.8 $$, what is the probability that two independent patients both recover?

Accepted Answer

$$ 0.8 	imes 0.8 = 0.64 $$

Question 13

A test score has a mean of $$ 100 $$ and a standard deviation of $$ 15 . $$What is the $$ z -$$score for a student who scored $$ 130 $$?

Accepted Answer

$$ z = \frac{130 - 100}{15} = 2 $$

Question 14

If a score has a $$ z -$$score of $$ -1.5  in a $$normal distribution, what does this indicate about the score's position relative to the mean?

Accepted Answer

The score is 1.5 standard deviations below the mean.

Question 15

In a normal distribution, what percentage of scores fall within one standard deviation of the mean?

Accepted Answer

About 68%

Question 16

Which concept explains why the distribution of sample means tends to be normal, even if the population distribution is not?

Accepted Answer

Central Limit Theorem

Question 17

A researcher collects 50 samples, each of size 30, from a population. What is the standard error of the mean if the population standard deviation is $$ 12 $$?

Accepted Answer

$$ \frac{12}{\sqrt{30}} \approx 2.19 $$

Question 18

Which of the following best describes a sample distribution of the mean?

Accepted Answer

A distribution of all possible means calculated from samples of a given size drawn from a population.

Question 19

A medical researcher wants to estimate the average blood pressure in adults. She randomly selects 100 adults and calculates the mean. Which statistical concept allows her to generalize her findings to the entire adult population?

Accepted Answer

Inferential statistics

Statistics Study Guide: Key Concepts and Methods

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