Question 1

A data set has a mean of 40. If you subtract 40 from every value and sum the results, what is the total?

Accepted Answer

$$0$$

Question 2

Which pair of measures are both resistant to extreme values (outliers)?

Accepted Answer

median and IQR

Question 3

A population has a larger standard deviation than another population measured in the same units. What does this indicate?

Accepted Answer

It has more dispersion.

Question 4

According to the Empirical Rule, about what percentage of data in a bell-shaped distribution lie within 3 standard deviations of the mean?

Accepted Answer

$$99.7\%$$

Question 5

An observation has a $$z-$$score of $$2.3. $$What does this mean?

Accepted Answer

It is $$2.3$$ standard deviations above the mean.

Question 6

Two variables are positively associated when:

Accepted Answer

as one variable increases, the other tends to increase

Question 7

A boxplot shows the median left of the center of the box and the right whisker much longer than the left. The distribution is:

Accepted Answer

skewed right

Question 8

If a distribution's shape is unknown, which tool can you use to describe the minimum percentage of data within $$k$$ standard deviations of the mean?

Accepted Answer

Chebyshev's inequality

Question 9

Which pair of variables would most likely have a negative correlation?

Accepted Answer

outside temperature and a home's heating bill

Question 10

Which value cannot be a linear correlation coefficient?

Accepted Answer

$$-1.3$$

Question 11

Which list is ordered from weakest to strongest linear association?

Accepted Answer

$$-0.10, 0.35, 0.60, -0.90$$

Question 12

A scatter diagram shows points forming a clear U-shape, and $$r = 0.02. $$Which conclusion is correct?

Accepted Answer

There is no linear relation, but there is a nonlinear relation.

Question 13

For a sample of $$n = 6$$, $$r = -0.92$$ and the critical value is $$0.811. $$What should you conclude?

Accepted Answer

A negative linear relation exists.

Question 14

In a contingency table, a marginal distribution is:

Accepted Answer

a frequency or relative frequency distribution of either the row or the column variable

Question 15

A coffee shop measures the weights (in grams) of ten espresso shots: $$8.2, 8.5, 8.5, 8.6, 8.7, 8.8, 9.0, 9.1, 9.2, 9.4. $$What is the sample mean?

Accepted Answer

$$8.8$$

Question 16

Scores on a standardized test are bell-shaped with mean $$75$$ and standard deviation $$5. $$What percentage of scores are between $$70$$ and $$80$$?

Accepted Answer

$$68\%$$

Question 17

Emma finished a 5K race in $$22$$ minutes (mean for women: $$26$$, $$SD = 3). $$Liam finished in $$20$$ minutes (mean for men: $$23$$, $$SD = 2). $$Who performed relatively better?

Accepted Answer

Liam, because his $$z-$$score is lower (more negative).

Question 18

A boxplot has a five-number summary: $$5, 8, 10, 16, 35. $$What is the interquartile range (IQR)?

Accepted Answer

$$8$$

Question 19

A college surveyed $$200$$ students about their age and class preference. $$120$$ prefer online classes. What proportion of all students prefer online classes, and is this a marginal or conditional proportion?

Accepted Answer

$$0.60$$, marginal

Question 20

A small business records monthly advertising spending ($$x) $$and sales ($$y). $$The correlation coefficient $$r is$$ $$0.968$$ for five months, but drops to $$0.067$$ after adding a sixth month with $$x = 1$$ and $$y = 90. $$What does this demonstrate?

Accepted Answer

Correlation is not resistant to outliers; a scatterplot is needed to detect such points.

Introductory Statistics Test 2 — Step-by-Step Study Guidance

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