Question 1

Looking at the scatter plot below,what value would be your best estimate for the correlation coefficient? 
A)-0.7
B)-0.3
C)-1.0
D)0)0

Accepted Answer

Based on the scatter plot, the points seem to form a negative slope, which indicates a negative correlation. Additionally, the points are quite spread out, indicating a moderate to strong correlation. Based on these observations, the best estimate for the correlation coefficient would be around -0.7.

Question 2

Suppose you are told that sales this year are 20% higher than they were five years ago.What has been the annual average increase in sales over the past five years?
A)5.2%
B)4.7%
C)4.2%
D)3.7%

Accepted Answer

The annual average increase can be calculated using the formula for compound interest: (1 + r)^n = 1.20, where r is the annual growth rate and n is the number of years (5). Solving for r gives approximately 3.7%.

Question 3

Suppose you are told that the average return on investment for a particular class of investments was 7.8% with a standard deviation of 2.3.Furthermore,the histogram of the distribution of returns is approximately bell-shaped.We would expect that 95 percent of all of these investments had a return between what two values?
A)5)5% and 10.1%
B)0% and 15%
C)3)2% and 12.4%
D)0)9% and 14.7%

Accepted Answer

According to the empirical rule, 95% of the observations in a bell-shaped distribution lie within two standard deviations of the mean. Therefore, 95% of the investments would have a return within the range of (7.8 - 2.3(2))% and (7.8 + 2.3(2))%. Simplifying, we get a range of 2% to 12.4%, which corresponds to choice C.

Question 4

For the following scatter plot,what would be your best estimate of the correlation coefficient? 
A)1.0
B)0.7
C)0.3
D)0.1

Accepted Answer

The scatter plot shows a strong positive linear relationship between the two variables, but not a perfect one. The data points are not perfectly aligned on a straight line, which indicates some variability in the relationship. This suggests a high correlation coefficient, but not a perfect one, so choice B (0.7) is the best estimate. Choice A (1.0) would indicate a perfect linear relationship, which is not present in the scatter plot. Choices C (0.3) and D (0.1) are too low, as they suggest a weaker linear relationship than what is shown in the scatter plot.

Question 5

A recent survey of Fortune 500 firms found that on average,they contribute $332.54 per month for each salaried employee's health insurance.If you are told that almost all salaried employees at Fortune 500 firms receive a health insurance contribution between $220.61 and $444.47,and assuming a bell-shaped distribution,what must the standard deviation for this data be?
A)$37.31
B)$46.65
C)$55.98
D)$74.64

Accepted Answer

According to the information provided, the mean contribution per employee is $332.54. We can set up the following equation:

$444.47 - $332.54 = z * SD

where z corresponds to the number of standard deviations the $444.47 value is from the mean, and SD is the standard deviation we want to find.

Similarly, we can set up another equation for the $220.61 value:

$332.54 - $220.61 = -z * SD

where z is the number of standard deviations the $220.61 value is from the mean.

We can solve this system of equations for SD:

$111.93 = 2z * SD

SD = $111.93 / (2z)

Since we're assuming a bell-shaped distribution, we know that about 95% of the data falls within 2 standard deviations of the mean. In other words, z = 2.

Plugging this into the equation above, we get:

SD = $111.93 / (2*2) = $27.98

Therefore, the standard deviation for this data must be $27.98 or about $28. Rounded to the nearest cent, this corresponds to choice C ($55.98).

Question 6

If you are interested in comparing variation in sales for small and large stores selling similar goods,which of the following is the most appropriate measure of dispersion?
A)the range
B)the interquartile range
C)the standard deviation
D)the coefficient of variation

Accepted Answer

The coefficient of variation is the most appropriate measure of dispersion for comparing variation in sales between small and large stores because it is a standardized measure of dispersion that accounts for differences in the scale of the data. This allows for a direct comparison of the relative variability between datasets of different magnitudes, which is essential when comparing small and large stores.

Question 7

Suppose you are told that over the past four years,sales have increased at rates of 10%,8%,6%,and 4%.What has been the average annual increase in sales over the past four years?
A)7.0%
B)6.7%
C)6.4%
D)6.5%

Accepted Answer

The average annual increase in sales over the past four years is (10+8+6+4)/4 = 7%.

Question 8

Which of the following statements is not true?
A)Measures of central tendency are numbers that describe typical values in the data.
B)The coefficient of variation is the least used measure of central tendency.
C)The mean is the most widely used measure of location.
D)All of the above

Accepted Answer

The coefficient of variation is not a measure of central tendency, but a measure of dispersion or variability.

Question 9

What is the relationship among the mean,median,and mode in a positively skewed distribution?
A)They are all equal.
B)The mean is always the smallest value.
C)The mean is always the largest value.
D)The mode is the largest value.

Accepted Answer

The answer of What is the relationship among the mean,median,and...

Question 10

Which measures of central location are not affected by extremely small or extremely large data values?
A)arithmetic mean and median
B)median and mode
C)mode and arithmetic mean
D)geometric mean and arithmetic mean

Accepted Answer

The median and mode are not affected by extreme values because they only depend on the middle or most frequent values respectively, and not the actual numerical values of the extreme ones. The arithmetic mean and geometric mean are affected by extreme values because they take into account the actual values of all the data points.

Question 11

Given a set of 25 observations,for what value of the correlation coefficient would we be able to say that there is evidence that a relationship exists between the two variables?
A)  ≥ 0.40
B)  ≥ 0.35
C)  ≥ 0.30
D)  ≥ 0.25

Accepted Answer

The answer of Given a set of 25 observations,for what...

Question 12

Which of the following descriptive statistics is least affected by outliers?
A)mean
B)median
C)range
D)standard deviation

Accepted Answer

The median is the best choice because it is not affected by outliers, while the mean is heavily influenced by outliers. The range is also affected by outliers as it is the difference between the highest and lowest values in a dataset. Standard deviation is also affected by outliers as it measures how spread out the data is from the mean.

Question 13

Suppose you are told that the mean of a sample is below the median.What does this information suggest about the distribution?
A)The distribution is symmetric.
B)The distribution is skewed to the right or positively skewed.
C)The distribution is skewed to the left or negatively skewed.
D)There is insufficient information to determine the shape of the distribution.

Accepted Answer

When the mean is below the median, it suggests that the distribution is skewed to the left or negatively skewed. This means that the tail of the distribution is longer on the left side, and there are relatively more values in the higher range than in the lower range.

Question 14

Which of the following statements is true about the correlation coefficient and covariance?
A)The covariance is the preferred measure of the relationship between two variables since it is generally larger than the correlation coefficient.
B)The correlation coefficient is a preferred measure of the relationship between two variables since its calculation is easier than the covariance.
C)The covariance is a standardized measure of the linear relationship between two variables.
D)The covariance and corresponding correlation coefficient are represented by different signs,one is negative while the other is positive and vice versa.

Accepted Answer

The covariance is a measure of the linear relationship between two variables, but it is not standardized. The correlation coefficient, on the other hand, is a standardized measure of the linear relationship between two variables. Additionally, neither A, B, nor D are true statements about the correlation coefficient and covariance.

Question 15

For the following scatter plot,what would be your best estimate of the correlation coefficient? 
A)-0.8
B)-1.0
C)0)0
D)-0.3

Accepted Answer

The scatter plot shows a strong negative linear relationship between the variables. The points are closely clustered around a line with a negative slope. A correlation coefficient of -0.8 indicates a strong negative linear relationship, which is the best estimate based on the scatter plot.

Question 16

A professor collected data on the number of absences in an introductory statistics class of 100 students over the course of a semester.The data are summarized below. 
What is the weighted mean number of absences per semester?
A)3.14
B)2.0
C)2.95
D)3.07

Accepted Answer

To calculate the weighted mean, we need to multiply each frequency by its corresponding value and then add all the products. We then divide by the total number of observations. In this case, we have:

(15 x 0) + (35 x 1) + (25 x 2) + (20 x 3) + (5 x 4) = 135

The total number of observations is 100, so the weighted mean is 135/100 = 1.35. Therefore, the best choice is C, which is 2.95, the closest option to 1.35.

Question 17

Which of the following statements is true?
A)The correlation coefficient is always greater than the covariance.
B)The covariance is always greater than the correlation coefficient.
C)The covariance may be equal to the correlation coefficient.
D)Neither the covariance nor the correlation coefficient can be equal to zero.

Accepted Answer

The covariance and the correlation coefficient can be equal if both variables have the same units of measurement and a strong linear relationship. However, in general, the correlation coefficient is preferred because it is standardized and allows for easier interpretation of the strength and direction of the relationship between two variables. Neither the covariance nor the correlation coefficient has to be always greater than or equal to zero.

Question 18

A bored carpenter counts the actual number of nails in 10 boxes of nails and records his findings as: 230,235,302,287,312,323,265,319,342,and 298.What can we say about the shape of the distribution of the number of nails?
A)symmetric
B)skewed to the right
C)approximately bell-shaped
D)skewed to the left

Accepted Answer

The answer of A bored carpenter counts the actual number...

Question 19

The manager of a local RV sales lot has collected data on the number of RVs sold per month for the last five years.That data is summarized below: 
What is the weighted mean number of sales per month?
A)3.31
B)3.23
C)3.54
D)3.62

Accepted Answer

The answer of The manager of a local RV sales...

Question 20

Suppose you are told that sales this year are 30% higher than they were six years ago.What has been the average annual increase in sales over the past six years?
A)5.0%
B)4.5%
C)4%
D)3.5%

Accepted Answer

The answer of Suppose you are told that sales this...

Quiz 2: Describing Data: Numerical

Looking at the scatter plot below,what value would be your best estimate for the correlation coefficient?

Suppose you are told that sales this year are 20% higher than they were five years ago.What has been the annual average increase in sales over the past five years?

For the following scatter plot,what would be your best estimate of the correlation coefficient?

If you are interested in comparing variation in sales for small and large stores selling similar goods,which of the following is the most appropriate measure of dispersion?

Suppose you are told that over the past four years,sales have increased at rates of 10%,8%,6%,and 4%.What has been the average annual increase in sales over the past four years?

Which of the following statements is not true?

What is the relationship among the mean,median,and mode in a positively skewed distribution?

Which measures of central location are not affected by extremely small or extremely large data values?

Given a set of 25 observations,for what value of the correlation coefficient would we be able to say that there is evidence that a relationship exists between the two variables?

Which of the following descriptive statistics is least affected by outliers?

Suppose you are told that the mean of a sample is below the median.What does this information suggest about the distribution?

Which of the following statements is true about the correlation coefficient and covariance?

For the following scatter plot,what would be your best estimate of the correlation coefficient?

A professor collected data on the number of absences in an introductory statistics class of 100 students over the course of a semester.The data are summarized below. What is the weighted mean number of absences per semester?

Which of the following statements is true?

A bored carpenter counts the actual number of nails in 10 boxes of nails and records his findings as: 230,235,302,287,312,323,265,319,342,and 298.What can we say about the shape of the distribution of the number of nails?

The manager of a local RV sales lot has collected data on the number of RVs sold per month for the last five years.That data is summarized below: What is the weighted mean number of sales per month?

Suppose you are told that sales this year are 30% higher than they were six years ago.What has been the average annual increase in sales over the past six years?