Math Problem Statement

  1. At what time was the temperature the highest?

a. 0900

b. 11:30

c. 1300

d. 1400

  1. In regression analysis the symbol r represents the_________________ and the symbol,

R2, represents the _________________.

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a. coefficient of determination; predicted value

b. coefficient of determination; Multiple coefficient of determination

c. Pearson-r coefficient; total variability of Y accounted for by all the Xs

d. variability of Y accounted for by one independent variable; summation

  1. Population median, population standard deviation, and the population mean are all

_________________.

a. measures of variability

b. examples of a parameter

c. measures of central tendency

d. examples of a statistic

  1. ∑(X – ) is _________________.

a. the sample standard deviation

b. equal to zero

c. the sum of squares of the deviations about the sample mean

d. the sample mean

  1. A professor asked his thirty students to take a statistics test. The scores from that test

ranged from 32 to 95, with a mean score of 75. The professor would like to determine

the average variability of the scores relative to the mean. Which statistical measure

would you ask him to use?

a. Pearson-r

b. Population mean

c. Standard deviation

d. Coefficient of determination

  1. The stem-and-leaf plot below shows how a class of sixth-graders scored on a math test. A score

of 63 or higher is passing. How many sixth-graders passed this math test?

a. 7

b. 13

c. 11

d. 17

  1. The z-score for a raw score of, 85, given that µ=105, and σ=10 is _________________.

a. 75

b. 2

c. -2

d. 20

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  1. A bar graph can be used to present _________________data, and a frequency polygon

can be used to present _________________ data.

a. nominal scale; ratio scale

b. ratio scale; interval scale

c. nominal scale; ordinal scale

d. independent; population

  1. A small company has 7 employees. The numbers of years these employees have

worked for this company are shown as follows:

4 14 3 16 9 8 16

Based upon this information, the median number of years that employees have been with this

company is:

a. 9 years

b. 16 years

c. 10 years

d. None of the above

  1. In terms of sampling distributions of the mean, as sample size increases the standard error

of the mean _________________.

a. tends to zero

b. increases

c. remains the same

d. decreases

  1. According to the box-and-whisker plot shown below, what is the third quartile value?

a. 70

b. 80

c. 90

d. 100

  1. An example of a ratio scale variable is _________________.

a. Age group

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b. English exam scores

c. Position in the Olympic 100m race

d. Number of children per household

  1. In the simple linear regression result, r2 =.47. What percentage of the variation in the

dependent variable is left UNEXPLAINED by the independent variable?

a. 53.0%

b. 47.0%

c. .47%

d. .53%

  1. A data point on a scratter plot _________________.

a. represents a pair of scores on the scatter plot

b. is synonymous with a single score

c. represents more than two values

d. represents a single value on the graph

  1. A professor took a sample of N=150 Wesley College students and found that the average

IQ was equal to 98 for this group. She then drew the conclusion that the average IQ was

equal to 98 for the entire population of students at Wesley’s College. This is an example of


.

a. probability

b. correlation

c. inferential statistics

d. descriptive statistics

Solution

Let's address each question one by one:

  1. At what time was the temperature the highest?

    • c. 1300
  2. In regression analysis, the symbol rr represents the __________________ and the symbol R2R^2 represents the _________________.

    • c. Pearson-r coefficient; total variability of Y accounted for by all the Xs
  3. Population median, population standard deviation, and the population mean are all __________________.

    • b. examples of a parameter
  4. (XXˉ)\sum(X - \bar{X}) is _________________.

    • b. equal to zero
  5. A professor asked his thirty students to take a statistics test. The scores from that test ranged from 32 to 95, with a mean score of 75. The professor would like to determine the average variability of the scores relative to the mean. Which statistical measure would you ask him to use?

    • c. Standard deviation
  6. The stem-and-leaf plot below shows how a class of sixth-graders scored on a math test. A score of 63 or higher is passing. How many sixth-graders passed this math test?

    • c. 11
  7. The z-score for a raw score of 85, given that μ=105\mu = 105 and σ=10\sigma = 10 is _________________.

    • c. -2
  8. A bar graph can be used to present _________________ data, and a frequency polygon can be used to present _________________ data.

    • a. nominal scale; ratio scale
  9. A small company has 7 employees. The numbers of years these employees have worked for this company are shown as follows: 4 14 3 16 9 8 16. Based upon this information, the median number of years that employees have been with this company is:

    • a. 9 years
  10. In terms of sampling distributions of the mean, as sample size increases the standard error of the mean _________________.

    • d. decreases
  11. According to the box-and-whisker plot shown below, what is the third quartile value?

    • b. 80
  12. An example of a ratio scale variable is _________________.

    • d. Number of children per household
  13. In the simple linear regression result, r2=0.47r^2 = 0.47. What percentage of the variation in the dependent variable is left UNEXPLAINED by the independent variable?

    • a. 53.0%
  14. A data point on a scatter plot _________________.

    • a. represents a pair of scores on the scatter plot
  15. A professor took a sample of N=150N = 150 Wesley College students and found that the average IQ was equal to 98 for this group. She then drew the conclusion that the average IQ was equal to 98 for the entire population of students at Wesley’s College. This is an example of _________________.

    • c. inferential statistics

Would you like any further details or have any questions about these answers?

Here are some related questions to explore the topics further:

  1. How do you calculate the Pearson-r coefficient in regression analysis?
  2. What is the difference between a parameter and a statistic in statistical terms?
  3. How is the standard deviation calculated from a given data set?
  4. What is the significance of a z-score in statistics?
  5. Can you explain the difference between nominal, ordinal, interval, and ratio scales?
  6. How do you interpret a box-and-whisker plot?
  7. What is the significance of the R2R^2 value in regression analysis?
  8. How can inferential statistics be used to make predictions about a population?

Tip: Understanding the context and proper application of different statistical measures is crucial for accurately interpreting data and drawing meaningful conclusions.

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Math Problem Analysis

Mathematical Concepts

Regression Analysis
Central Tendency
Variability
Probability

Formulas

Standard Deviation formula
Z-score formula

Theorems

Central Limit Theorem
Regression Analysis Theorems

Suitable Grade Level

College Level