Question 1

A biology professor claimed that the proportions of grades in his classes are the same. A sample of 100 students showed the following frequencies. $$\begin{array} { | l | c | c | c | c | c | } 
\hline \text { Grade } & \text { A } & \text { B } & \text { C } & \text { D } & \text { F } \
\hline \text { Frequency } & 14 & 23 & 27 & 26 & 10 \
\hline
\end{array}$$ Do the data provide enough evidence to support the professor's claim?

Accepted Answer

The answer of A biology professor claimed that the proportions...

Question 2

Which of the following should be used if we want to conduct a two-tail test of a population proportion?

Accepted Answer

A)  z-test of a population proportion. 
B)  Chi-squared test of a binomial experiment since $z ^ { 2 } = \chi ^ { 2 }$ . 
C)  the chi-squared test of a contingency table. 
D)  z-test of a population proportion and Chi-squared test of a binomial experiment since $z ^ { 2 } = \chi ^ { 2 }$ . 
E)  Chi-squared test of a binomial experiment since $z ^ { 2 } = \chi ^ { 2 }$ and the chi-squared test of a contingency table.

Question 3

In a chi-squared goodness-of-fit test, if the expected frequencies $e _ { i }$ and the observed frequencies $f _ { i }$ were quite different, which of the following is the best conclusion?

Accepted Answer

A)  Null hypothesis is false, and reject Ho. 
B)  Null hypothesis is true, and retain Ho. 
C)  Alternative hypothesis is false, reject HA. 
D)  Chi-squared distribution is invalid, use t-distribution instead.

Question 4

Which of the following best describes the degrees of freedom needed in a Chi-squared test for normality?

Accepted Answer

A)  Number of intervals used to test the hypothesis minus 1. 
B)  Number of parameters estimated minus 1. 
C)  Number of intervals used to test the hypothesis minus the number of parameters estimated minus 1. 
D)  Number of intervals used to test the hypothesis minus the number of parameters estimated minus 2.

Question 5

An Australian tyre manufacturer operates a plant in Melbourne and another plant in Adelaide. Employees at each plant have been evenly divided among three issues (wages, working conditions and super benefits) in terms of which one they feel should be the primary issue in the upcoming contract negotiations. The secretary of the union has recently circulated pamphlets among the employees, attempting to convince them that super benefits should be the primary issue. A subsequent survey revealed the following breakdown of the employees according to the plant at which they worked and the issue that they felt should be supported as the primary one. $\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\text { Issues }$
$\begin{array} { | l | c | c | c | } 
\hline \text { Plant Location } & \text { Very interesting } & \text { Fairly interesting } & \text { Not interesting } \
\hline \text { Melbourne } & 60 & 62 & 78 \
\hline \text { Adelaide } & 70 & 56 & 74 \
\hline
\end{array}$ Can you infer at the 5% significance level that the proportional support by the employees at both plants for the issues has changed since the pamphlet was circulated?

Accepted Answer

The answer of An Australian tyre manufacturer operates a plant...

Question 6

In 2003, computers of Brand A controlled 25% of the market, Brand B 20%, Brand C 10% and Brand D 45%. In 2004, sample data were collected from many randomly selected stores throughout the country. Of the 1200 computers sold, 280 were Brand A, 270 were Brand B, 90 were Brand C and 560 were Brand D. Has the market changed since 2003? Test at the 1% significance level.

Accepted Answer

The answer of In 2003, computers of Brand A controlled...

Question 7

A left-tailed area in the chi-squared distribution equals 0.90. For 10 degrees of freedom, the table value equals 15.9871.

Accepted Answer

A) True 
 B)False

Question 8

A university lecturer had the following semester 1 student's final grades for the course that they teach: 8% High Distinction, 35% Distinction, 40% Credit, 12% Pass, and 5% Failed. A sample of 100 second semester final grades for the same course showed 12 High distinctions, 30 Distinctions, 35 Credits, 15 Passes, and 8 Fails. Test at the 10% significance level to determine whether the semester one grades differ significantly from the semester two grades.

Accepted Answer

The answer of A university lecturer had the following semester...

Question 9

A chi-squared test of a contingency table with 4 rows and 4 columns shows that the value of the test statistic is 23. Which of the following best describes the p-value for this test?

Accepted Answer

A)  p-value  0.10 
D)  0.005 < p-value < 0.01

Question 10

In a chi-squared test of a contingency table, the value of the test statistic was $\chi ^ { 2 } = 12.678$ , the significance level was $\alpha$ = 0.05 and the degrees of freedom was 6. Thus:

Accepted Answer

A)  we fail to reject the null hypothesis at $\alpha$ = 0.05. 
B)  we reject the null hypothesis at $\alpha$ = 0.05. 
C)  we don't have enough evidence to accept or reject the null hypothesis at $\alpha$= 0.05. 
D)  we should increase the level of significance in order to reject the null hypothesis.

Question 11

A multinomial experiment, where the outcome of each trial can be classified into one of two categories, is identical to the binomial experiment.

Accepted Answer

A) True 
 B)False

Question 12

In chi-squared tests, the conventional and conservative rule - known as the rule of five - is to require that the:

Accepted Answer

A)  expected frequency for each cell be at least 5. 
B)  number of degrees of freedom for the test be at least 5. 
C)  each expected and observed frequency be at least 5. 
D)  difference between the observed and expected frequency for each cell be at least 5.

Question 13

Which statistical technique is appropriate when we describe a single population of nominal data with exactly two categories?

Accepted Answer

A)  Zz-test of a population proportion. 
B)  Chi-squared test of a multinomial experiment. 
C)  Chi-squared test of a contingency table. 
D)  Z-test of a population proportion and Chi-squared test of a multinomial experiment. 
E)  Chi-squared test of a multinomial experiment and Chi-squared test of a contingency table.

Question 14

Consumer panel preferences for three proposed fast food restaurants are as follows: $$\begin{array} { | c | c | c | } 
\hline \text { Restaurant } \mathrm { A } & \text { Restaurant B } & \text { Restaurant C } \
\hline 48 & 62 & 40 \
\hline
\end{array}$$ Using the 0.05 level of significance, test to see if there is a preference among the three restaurants.

Accepted Answer

The answer of Consumer panel preferences for three proposed fast...

Question 15

In a goodness-of-fit test, suppose that a sample showed that the observed frequency $f _ { i }$ and expected frequency $e _ { i }$ were equal for each cell i. Which of the following best describes the decision for the hypothesis test?

Accepted Answer

A)  Reject Ho at α of 0.05 but retain Ho at α of 0.025. 
B)  Reject Ho at any level of α. 
C)  Retain Ho at any level of α. 
D)  Retain Ho at α of 0.05 but reject Ho at α of 0.025.

Question 16

A biology professor claimed that the proportions of grades in his classes are the same. A sample of 100 students showed the following frequencies. $$\begin{array} { | l | c | c | c | c | c | } 
\hline \text { Grade } & \text { A } & \text { B } & \text { C } & \text { D } & \text { F } \
\hline \text { Frequency } & 14 & 23 & 27 & 26 & 10 \
\hline
\end{array}$$ Use statistical software to compute the p-value for this test.

Accepted Answer

The answer of A biology professor claimed that the proportions...

Question 17

The number of cars sold by three salespersons over a 3-month period are shown below: $$\begin{array} { | l | c  c  c | } 
\hline & { \text { Brand of Car } } \
\hline \text { Salesperson } & \text { Brand } \mathrm { A } & \text { Brand B } & \text { Brand C } \
\hline \text { David } & 7 & 2 & 6 \
\hline \text { Edward } & 11 & 4 & 8 \
\hline \text { Frank } & 8 & 5 & 3 \
\hline
\end{array}$$ Using the 5% level of significance, test for the independence of salesperson and type of product sold.

Accepted Answer

The answer of The number of cars sold by three...

Question 18

A particular insurance company wants to investigate whether the gender and age of a client are related. A random sample of 350 clients of this insurance company was taken. $\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\text { Age group } $ 
$\begin{array} { | l | c|c | c | } 
\hline & 25 \text { and under } & \begin{array} { c } 
\text { Over } 25 \text { and } \
\text { under } 50
\end{array} & 50 \text { and over } \
\hline \text { Male } & 35 & 60 & 68 \
\hline \text { Female } & 65 & 80 & 42 \
\hline
\end{array}$ Conduct a test to determine whether gender and age group are independent, using $\alpha$ of 0.01.

Accepted Answer

The answer of A particular insurance company wants to investigate...

Question 19

If we want to perform a one-tail test for differences between two populations of nominal data with exactly two categories, we must employ the z-test of $p _ { 1 } - p _ { 2 }$ .

Accepted Answer

A) True 
 B)False

Question 20

A right-tailed area in the chi-squared distribution equals 0.01. For 4 degrees of freedom, the table value equals 13.2767.

Accepted Answer

A) True 
 B)False

Exam 17: Additional Tests for Nominal Data: Chi-Squared Tests

Which of the following should be used if we want to conduct a two-tail test of a population proportion?

In a chi-squared goodness-of-fit test, if the expected frequencies eie _ { i }ei​ and the observed frequencies fif _ { i }fi​ were quite different, which of the following is the best conclusion?

Which of the following best describes the degrees of freedom needed in a Chi-squared test for normality?

A left-tailed area in the chi-squared distribution equals 0.90. For 10 degrees of freedom, the table value equals 15.9871.

A chi-squared test of a contingency table with 4 rows and 4 columns shows that the value of the test statistic is 23. Which of the following best describes the p-value for this test?

In a chi-squared test of a contingency table, the value of the test statistic was χ2=12.678\chi ^ { 2 } = 12.678χ2=12.678 , the significance level was α\alphaα = 0.05 and the degrees of freedom was 6. Thus:

A multinomial experiment, where the outcome of each trial can be classified into one of two categories, is identical to the binomial experiment.

In chi-squared tests, the conventional and conservative rule - known as the rule of five - is to require that the:

Which statistical technique is appropriate when we describe a single population of nominal data with exactly two categories?

In a goodness-of-fit test, suppose that a sample showed that the observed frequency fif _ { i }fi​ and expected frequency eie _ { i }ei​ were equal for each cell i. Which of the following best describes the decision for the hypothesis test?

If we want to perform a one-tail test for differences between two populations of nominal data with exactly two categories, we must employ the z-test of p1−p2p _ { 1 } - p _ { 2 }p1​−p2​ .

A right-tailed area in the chi-squared distribution equals 0.01. For 4 degrees of freedom, the table value equals 13.2767.

In a chi-squared goodness-of-fit test, if the expected frequencies $e _ { i }$ and the observed frequencies $f _ { i }$ were quite different, which of the following is the best conclusion?

In a chi-squared test of a contingency table, the value of the test statistic was $\chi ^ { 2 } = 12.678$ , the significance level was $\alpha$ = 0.05 and the degrees of freedom was 6. Thus:

In a goodness-of-fit test, suppose that a sample showed that the observed frequency $f _ { i }$ and expected frequency $e _ { i }$ were equal for each cell i. Which of the following best describes the decision for the hypothesis test?

If we want to perform a one-tail test for differences between two populations of nominal data with exactly two categories, we must employ the z-test of $p _ { 1 } - p _ { 2 }$ .