Question 1

A coffee machine sales representative visits 5 businesses per day. A sample of 200 days gives the frequencies of coffee machine sales volumes listed below: $$\begin{array} { | c | c | } 
\hline \text { Number of sales } & \text { Observed frequency (days) } \
\hline 0 & 10 \
\hline 1 & 38 \
\hline 2 & 69 \
\hline 3 & 63 \
\hline 4 & 18 \
\hline 5 & 2 \
\hline
\end{array}$$ Assume that the population is binomially distributed with a probability of purchase p = 0.50.
Should the assumption of a binomial distribution be rejected at the 1% significance level?

Accepted Answer

The answer of A coffee machine sales representative visits 5...

Question 2

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 3

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

Accepted Answer

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

Question 4

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. $$\begin{array} { | l | c | c | c | } 
\hline & & { \text { Issues } } \
\hline \text { Plant Location } & \text { Very interesting } & \text { Fairly interesting } & \text { Not interesting } \
\hline \text { Melbourne } & 60 & 62 & 78 \
\hline \text { Adel aide } & 70 & 56 & 74 \
\hline
\end{array}$$ Can you infer at the 5% significance level that the proportional support by the Melbourne employees for the three issues has changed since the pamphlet was circulated?

Accepted Answer

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

Question 5

Consider a multinomial experiment involving n = 200 trials and k = 5 cells. The observed frequencies resulting from the experiment are shown in the following table. $$\begin{array} { | l | c | c | c | c | c | } 
\hline \text { Cell } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Frequency } & 4 & 11 & 14 & 12 & 9 \
\hline
\end{array}$$ The null hypothesis to be tested is as follows. $H _ { 0 } : p _ { 1 } = 0.10$ , $p _ { 2 } = 0.25,$ $p _ { 3 } = 0.30,$ $p _ { 4 } = 0.20,$ $p _ { 5 } = 0.15$ $p _ { 5 } = 0.15$ .

Accepted Answer

The answer of Consider a multinomial experiment involving n =...

Question 6

A biology professor claimed that the proportions of grades in his classes are the same $$\begin{array} { | l | c | c | c | c | c | } 
\hline \text { Grade } & \text { A } & \text { B } & \text { C } & \text { D } & \text { F } \
\hline \text { Frequency } & 14 & 23 & 27 & 26 & 10 \
\hline
\end{array}$$ State the null and alternative hypotheses to be tested.

Accepted Answer

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

Question 7

In a number of universities in Australia, lecture recordings online are provided to all students. There is
growing concern amongst teaching staff that lecture recordings are used as a substitute for lecture
attendance and that this is leading to a greater fail rate.
At one particular university, a random sample of 224 students is taken, where the students are asked if
they attended the majority of lectures for the last exam they took, or if they viewed the majority of
lecture recordings online and then the student's records are followed up to see if the student passed
that course. $$\begin{array} { | c | c | c | } 
\hline & \text { Attended lectures } & \text { Viewed lecture recordings online } \
\hline \text { Fail } & 40 & 80 \
\hline \text { Pass } & 56 & 48 \
\hline
\end{array}$$ Conduct a test to determine if enough evidence exists to infer that lecture attendance and passing a
university course are related. Test at the 10% level of significance.

Accepted Answer

The answer of In a number of universities in Australia,...

Question 8

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. $$\begin{array} { | l | c | c | c | } 
\hline && { \text { Age group } } \
\hline & 25 \text { and under } & \begin{array} { c } 
\text { Over } 25 \text { and } \
\text { under } 50
\end{array} & 50 \text { and over } \
\hline \text { Male } & 35 & 60 & 68 \
\hline \text { Female } & 65 & 80 & 42 \
\hline
\end{array}$$ Conduct a test to determine whether gender and age group are independent, using α of 0.01.

Accepted Answer

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

Question 9

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. $$\begin{array} { | l | c | c | c | } 
\hline & & { \text { Issues } } \
\hline \text { Plant Location } & \text { Very interesting } & \text { Fairly interesting } & \text { Not interesting } \
\hline \text { Melbourne } & 60 & 62 & 78 \
\hline \text { Adel aide } & 70 & 56 & 74 \
\hline
\end{array}$$ 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 10

A biology professor claimed that the proportions of grades in his classes are the same. A sample of 100 students showed the following frequencies. $$\begin{array} { | l | c | c | c | c | c | } 
\hline \text { Grade } & \text { A } & \text { B } & \text { C } & \text { D } & \text { F } \
\hline \text { Frequency } & 14 & 23 & 27 & 26 & 10 \
\hline
\end{array}$$ Determine the rejection region at the 5% significance level.

Accepted Answer

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

Question 11

Consider a multinomial experiment involving n = 200 trials and k = 5 cells. The observed frequencies resulting from the experiment are shown in the following table: $$\begin{array} { | l | c | c | c | c | c | } 
\hline \text { Cell } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Frequency } & 8 & 22 & 28 & 24 & 18 \
\hline
\end{array}$$ The null hypothesis to be tested is as follows. $H _ { 0 } : p _ { 1 } = 0.10$ , $p _ { 2 } = 0.25,$ $p _ { 3 } = 0.30,$ $p _ { 4 } = 0.20,$ $p _ { 5 } = 0.15$ $p _ { 5 } = 0.15$ .

Accepted Answer

The answer of Consider a multinomial experiment involving n =...

Question 12

A salesperson makes five calls per day. A sample of 200 days gives the frequencies of sales volumes listed below: $$\begin{array} { | c | c | } 
\hline \text { Number of sales } & \text { Observed frequency (days) } \
\hline 0 & 10 \
\hline 1 & 38 \
\hline 2 & 69 \
\hline 3 & 63 \
\hline 4 & 18 \
\hline 5 & 2 \
\hline
\end{array}$$ Assume that the population is binomially distributed with a probability of purchase p = 0.50.
Compute the expected frequencies for x = 0, 1, 2, 3, 4 and 5 by using the binomial probability function or the binomial tables. Combine categories if necessary to satisfy the rule of five.

Accepted Answer

The answer of A salesperson makes five calls per day....

Question 13

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. $$\begin{array} { | l | c | c | c | } 
\hline &&{ \text { Issues } } \
\hline \text { Plant Location } & \text { Very interesting } & \text { Fairly interesting } & \text { Not interesting } \
\hline \text { Melbourne } & 60 & 62 & 78 \
\hline \text { Adel aide } & 70 & 56 & 74 \
\hline
\end{array}$$ Can you infer at the 5% significance level that the proportional support by the Adelaide employees for the three issues has changed since the pamphlet was circulated?

Accepted Answer

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

Question 14

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 15

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. $$\begin{array} { | l | c | c | c | } 
\hline && { \text { Issues } } \
\hline \text { Plant Location } & \text { Very interesting } & \text { Fairly interesting } & \text { Not interesting } \
\hline \text { Melbourne } & 60 & 62 & 78 \
\hline \text { Adel aide } & 70 & 56 & 74 \
\hline
\end{array}$$ Do the data indicate at the 5% significance level that there are differences between the two plants regarding which issue should be the primary one?

Accepted Answer

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

Question 16

A psychologist claims that people who exercise regularly are more content with their body image. A random sample of 102 people was taken, where they were asked if they regularly exercise and if they were content with their body image. $$\begin{array} { | l | l | l | } 
\hline & \text { Not content } & \text { Content } \
\hline \text { Exercised regularly } & 20 & 30 \
\hline \begin{array} { l } 
\text { Did not exercise } \
\text { regularly }
\end{array} & 28 & 24 \
\hline
\end{array}$$ Is there significant evidence to support this claim? Test at the 1% significance level.

Accepted Answer

The answer of A psychologist claims that people who exercise...

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