Question 1

Suppose a Normal model describes the number of pages printer ink cartridges last. If we keep track of printed pages for the 47 printers at a company's office, which must be true?
I. The page counts for those ink cartridges will be normally distributed. II. The histogram for those page counts will be symmetric.
III. 95% of those page counts will be within 2 standard deviations of the mean.

Accepted Answer

The assumption that the data will be normally distributed or that the histogram will be symmetric is not necessarily true just because a normal model is used to describe the data. The statement about 95% of the data being within 2 standard deviations of the mean is a characteristic of a normal distribution, but without confirming the data actually follows a normal distribution closely, this cannot be assumed to be true for the specific case of the 47 printers.

Question 2

Your Stats teacher tells you your test score was the 3rd quartile for the class. Which is true?
I. You got 75% on the test.
II. You can't really tell what this means without knowing the standard deviation.
III. You can't really tell what this means unless the class distribution is nearly Normal.

Accepted Answer

Being in the 3rd quartile means your score was higher than 75% of the class, not that you got a 75% score. The 3rd quartile's interpretation doesn't depend on knowing the standard deviation or the distribution being nearly Normal.

Question 3

Which is true of the data whose distribution is shown? 
 
I. The distribution is skewed to the right.
II. The mean is probably smaller than the median.
III. We should summarize with median and IQR.

Accepted Answer

The answer of Which is true of the data whose...

Question 4

Which is true of the data shown in the histogram?
 
 I. The distribution is approximately symmetric.
II. The mean and median are approximately equal.
III. The median and IQR summarize the data better than the mean and standard deviation.

Accepted Answer

The answer of Which is true of the data shown...

Question 5

Which of the following summaries are changed by adding a constant to each data value?
I. the mean
II. the median
III. the standard deviation

Accepted Answer

Adding a constant to each data value will shift the entire data set to the right or left but will not change the relative order of the values, so the median will also be shifted by the same constant. However, the standard deviation measures the spread of the data set around the mean, so adding a constant to each value will also add the same constant to the mean, increasing the distance of each value from the mean and therefore increasing the standard deviation.

Question 6

The mean number of hours worked for the 30 males was 6, and for the 20 females was 9. The overall mean number of hours worked…

Accepted Answer

To find the overall mean, you multiply the mean hours by the number of individuals in each group and then divide by the total number of individuals. For males: 6 hours * 30 males = 180 hours. For females: 9 hours * 20 females = 180 hours. Total hours = 360 hours. Total individuals = 30 males + 20 females = 50 individuals. Overall mean = 360 hours / 50 individuals = 7.2 hours.

Question 7

The ages of people attending the opening show of a new movie are summarized in the ogive shown. Estimate the IQR of the ages.

Accepted Answer

To estimate the IQR, we must first find the median, Q1, and Q3 values. From the ogive, we can estimate the median to be around 40 years old. To approximate Q1, we find the 25th percentile, which is approximately 32 years old. To approximate Q3, we find the 75th percentile, which is approximately 45 years old.

Therefore: 
Median = 40
Q1 = 32
Q3 = 45

We can now calculate the IQR: 
IQR = Q3 - Q1 
IQR = 45 - 32 
IQR = 13

Therefore, the estimated IQR of the ages is 13, which corresponds to choice C.

Question 8

Which is true of the data whose distribution is shown?
I. The distribution is skewed to the right.
II. The mean is probably smaller than the median.
III. We should summarize with mean and standard deviation.

Accepted Answer

The answer of Which is true of the data whose...

Question 9

The SPCA has kept these data records for the past 20 years. If they want to show the trend in the number of dogs they have housed, what kind of plot should they make?

Accepted Answer

A timeplot would show the trend over the 20 years by plotting the number of dogs housed on the y-axis and the year on the x-axis, allowing for a clear visual display of any patterns or changes over time. Pie charts are more appropriate for displaying proportions of a whole, bar graphs are good for displaying comparisons between categorical variables, histograms for continuous numerical data, and boxplots for summarizing the distribution of numerical data.

Question 10

Suppose that a Normal model describes the acidity (pH) of rainwater, and that water tested after last week's storm had a z-score of 1.8. This means that the acidity of that rain…

Accepted Answer

A z-score of 1.8 means the observation is 1.8 standard deviations above the mean of the Normal distribution. In this case, the observation refers to the pH of rainwater, so the rainwater tested had a pH that was 1.8 standard deviations higher than the average pH of rainwater. Therefore, the answer is D.

Question 11

Two sections of a class took the same quiz. Section A had 15 students who had a mean score of 80, and Section B had 20 students who had a mean score of 90. Overall, what was the approximate mean score for all of the students on the quiz?

Accepted Answer

The total number of students is 15 + 20 = 35. The total score is 15 * 80 + 20 * 90 = 1200 + 1800 = 3000. Therefore, the mean score is 3000 / 35 = 85.71428571428571. Rounded to the nearest tenth, the answer is 85.7.

Question 12

Which is true of the data shown in the histogram?
I. The distribution is skewed to the right.
II. The mean is probably smaller than the median.
III. We should use median and IQR to summarize these data.

Accepted Answer

From the histogram, we can see that the majority of the bars are on the left side, with very few on the right side. This indicates a skew to the right, so statement I is true. Additionally, the median is likely closer to the center of the distribution (towards the left), while there are a few high values that pull the mean towards the right. Therefore, statement II is also true. Finally, because of the skewness, it is best to use the median and IQR as summary statistics instead of the mean and standard deviation. Therefore, statement III is also true.

Question 13

Environmental researchers have collected rain acidity data for several decades. They want to see if there is any evidence that attempts to reduce industrial pollution have produced a trend toward less acidic rainfall. They should display their data in a(n)…

Accepted Answer

A timeplot is the best choice as it allows for the visualization of any trends over time, as well as any potential seasonality or cyclical patterns in the data. The other options (contingency table, histogram, bar graph, and boxplot) are not appropriate for displaying trends over time.

Question 14

We might choose to display data with a stemplot rather than a boxplot because a stemplot
I. reveals the shape of the distribution.
II. is better for large data sets. III. displays the actual data.

Accepted Answer

A stemplot displays the actual data, allowing us to see the distribution of the data (I), and it is suitable for small to medium-sized data sets (III). Boxplots are better for large data sets (II), but they do not display the actual data as stemplots do. Therefore, D is the best choice as it acknowledges the advantages of stemplots in revealing the distribution and displaying actual data, while also noting that boxplots might be better for larger data sets.

Question 15

The veterinary bills for the dogs are summarized in the ogive below. Estimate the IQR of these expenses.

Accepted Answer

The answer of The veterinary bills for the dogs are...

Quiz 1: Stats Start Here

Your Stats teacher tells you your test score was the 3rd quartile for the class. Which is true? I. You got 75% on the test. II. You can't really tell what this means without knowing the standard deviation. III. You can't really tell what this means unless the class distribution is nearly Normal.

Which is true of the data whose distribution is shown? I. The distribution is skewed to the right. II. The mean is probably smaller than the median. III. We should summarize with median and IQR.

Which is true of the data shown in the histogram? I. The distribution is approximately symmetric. II. The mean and median are approximately equal. III. The median and IQR summarize the data better than the mean and standard deviation.

Which of the following summaries are changed by adding a constant to each data value? I. the mean II. the median III. the standard deviation

The mean number of hours worked for the 30 males was 6, and for the 20 females was 9. The overall mean number of hours worked…

The ages of people attending the opening show of a new movie are summarized in the ogive shown. Estimate the IQR of the ages.

Which is true of the data whose distribution is shown? I. The distribution is skewed to the right. II. The mean is probably smaller than the median. III. We should summarize with mean and standard deviation.

The SPCA has kept these data records for the past 20 years. If they want to show the trend in the number of dogs they have housed, what kind of plot should they make?

Suppose that a Normal model describes the acidity (pH) of rainwater, and that water tested after last week's storm had a z-score of 1.8. This means that the acidity of that rain…

Two sections of a class took the same quiz. Section A had 15 students who had a mean score of 80, and Section B had 20 students who had a mean score of 90. Overall, what was the approximate mean score for all of the students on the quiz?

Which is true of the data shown in the histogram? I. The distribution is skewed to the right. II. The mean is probably smaller than the median. III. We should use median and IQR to summarize these data.

Environmental researchers have collected rain acidity data for several decades. They want to see if there is any evidence that attempts to reduce industrial pollution have produced a trend toward less acidic rainfall. They should display their data in a(n) …

We might choose to display data with a stemplot rather than a boxplot because a stemplot I. reveals the shape of the distribution. II. is better for large data sets. III. displays the actual data.

The veterinary bills for the dogs are summarized in the ogive below. Estimate the IQR of these expenses.