# mathematics

## Practice Set 5

1. This distribution hasonlyoneparameter.Thecurveisskewedtotherightforsmall*df*and

becomessymmetricforlarge*df*.The entiredistributioncurveliestotherightofthevertical

axis.Thedistributionassumes nonnegativevaluesonly

- t distribution
- Normal distribution
- Chi-square distribution
- Linear regression.

2. Find the value of x2 for 12 degrees of freedom and an area of .025 in the right tail of the chi-

square distribution curve. What is the value of chi-square? Round to three decimal places

3. Determine the value of x2 for 14 degrees of freedom and an area of .10 in the left tail of the

chi-square distribution curve. What is the value of chi-square? Round to three decimal places

4. Determine the value of x2 for 23 degrees of freedom and an area of .990 in the left tail of the

chi-square distribution curve. What is the value of chi-square? Round to three decimal places.

5. Α ____________ compares the observed frequencies from a multinomial experiment with

expected frequencies derived from a certain pattern or theoretical distribution. The test

evaluates how well the observed frequencies fit the expected frequencies.

A. Goodness-of-fit test

B. Chi-square test

C. Linear regression

6. The __________ are the frequencies obtained from the performance of a

multinomial experiment. The expected frequencies are the frequencies that we expect to obtain

if the null hypothesis is true.

A. Observed frequencies

B. Expected frequencies

C. Fluctuating frequencies

7. The expected frequency of a category is given by Ε = np where n is the sample size and p is the

probability that an element belongs to that category if the null hypothesis is true. The

________ for a goodness–of–fit test are k – 1, where k denotes the number of possible

outcomes (or categories) for the experiment.

A. Number of observations

B. Degrees of freedom

C. Total population

8. Thismodelincludesonlytwovariables,oneindependentandonedependent,iscalleda _____1______. The**___2____**istheonebeingexplained,andthe **___3___**is theoneusedtoexplainthevariationinthedependentvariable. Select the correct letter that would make the sentence true.

1. Select a letter from the list to make this statement true.

2. Select a letter from the list to make this statement true.

3. Select a letter from the list to make this statement true.

A. Linear model

B. Qualitative variable

C. Multivariate analysis of variance

D. Independent variable

E. Simple regression model

F. One-way Analysis of Variance

G. Dependent variable

H. Quantitative variable

9. A population data set produced the following information.

N=460, ∑x=3920, ∑y=2650, ∑xy=26,570, ∑x2=48,530

Find the population regression line. Round to three decimal places. Use the format as an example when submitting your equation 456.123 + 789.123x

10. The following information is obtained from a sample data set.

n=12, ∑x=66, ∑y=588, ∑xy=2244, ∑x2=396

Find the estimated regression line Use this format as an example when submitting your equation 123 – 45x