BUS 204 Week 13 Assignment

BUS 204 Week 13 Assignment | MiraCosta College

1.

In the hypothesis test to determine if ergonomic keyboards increase the average words per minute, what was the critical value for this upper tailed test? Round your answer to two decimal places.

 2.822.82

2.

To perform a test of the null and alternative hypotheses shown below, random samples were selected from the two normally distributed populations with equal variances. The data are shown below. Test the null hypothesis using an alpha level equal to

0.05.

H0:

μ1−μ2=0

HA:

μ1−μ2≠0              Sample from Population 1            Sample from Population 2           

                36           40           26           36           34           33           44           37           38           31          

                35           29           37           40           39           37           34           38           35           32          

Determine the rejection region for the test statistic t. Select the correct choice below and fill in the answer box(es) to complete your choice.

A.

t< nothing

B.

t> nothing

C.

t< negative 2.1009−2.1009

or

t> 2.10092.1009

Calculate the value of the test statistic.

t=

Since the test statistic

is not

in the rejection region,

do not reject

the null hypothesis. There is

insufficient

evidence to conclude that the two population means are different.

3.

Given the null and alternative hypotheses, sample means, sample sizes, and population standard deviations shown to the right, conduct a hypothesis test using an alpha level equal to

0.05.      H0:

μ1−μ2≥0

 HA:

μ1−μ2<0              x1           =             132         x2           =             147

                                σ1           =             12           σ2           =             11

                                n1           =             55           n2           =             45

Determine the rejection region for the test statistic z. Select the correct choice below and fill in the answer box to complete your choice.

(Round to

three

decimal places as needed.)

A.

z> nothing

B.

z< nothing

or

z> nothing

C.

z< negative 1.645−1.645

Your answer is correct.

Calculate the value of the test statistic.

z= negative 6.51−6.51

Since the test statistic

is

in the rejection region,

reject

the null hypothesis. There is

sufficient

evidence to conclude that the mean of population 1 is

less

than the mean of population 2.

4.

A job-placement firm would like to know if the average starting salary in a particular year for chemical engineering majors is higher than the average starting salary in that same year for electrical engineering majors. To conduct its test, the job-placement firm has selected a random sample of

124

electrical engineering majors and

110

chemical engineering majors who graduated and received jobs in that year. Each graduate was asked to report his or her starting salary. The results of the survey are below. Complete parts a and b.

Click the icon for the results of the survey.

a. Conduct a hypothesis test at the

0.10

level of significance to determine whether the mean starting salary for chemical engineering graduates was higher than the mean starting salary for electrical engineering graduates. Assume the populations from which the samples were taken are approximately normally distributed with equal variances.

Let

μ1

be the population mean starting salary for chemical engineering graduates, and

μ2

be the population mean starting salary for electrical engineering students. State the null and alternative hypotheses.

A.

H0:

μ1−μ2=0

HA:

μ1−μ2≠0

B.

H0:

μ1−μ2≠0

HA:

μ1−μ2=0

C.

H0:

μ1−μ2≤0

HA:

μ1−μ2>0

D.

H0:

μ1−μ2<0

HA:

μ1−μ2≥0

Calculate the test statistic.

The test statistic is

Calculate the p-value.

The p-value is

 00.

State the conclusion for this hypothesis test.

A.

Reject

H0.

There

is not

sufficient evidence at the

α=0.10

level of significance to conclude that chemical engineering graduates were paid more.

B.

Reject

H0.

There

is

sufficient evidence at the

α=0.10

level of significance to conclude that chemical engineering graduates were paid more.

Your answer is correct.

C.

Do not reject

H0.

There

is

sufficient evidence at the

α=0.10

level of significance to conclude that chemical engineering graduates were paid more.

D.

Do not reject

H0.

There

is not

sufficient evidence at the

α=0.10

level of significance to conclude that chemical engineering graduates were paid more.

b. Conduct a hypothesis test at the

0.10

level of significance to determine whether a difference exists in the starting salaries for the two groups. Do not assume that the populations from which the samples were taken have equal variance.

State the null and alternative hypotheses.

A.

H0:

μ1−μ2≠0

HA:

μ1−μ2=0

B.

H0:

μ1−μ2<0

HA:

μ1−μ2≥0

C.

H0:

μ1−μ2=0

HA:

μ1−μ2≠0

D.

H0:

μ1−μ2≤0

HA:

μ1−μ2>0

Calculate the test statistic.

The test statistic is

Calculate the p-value.

The p-value is

State the conclusion for this hypothesis test.

A.

Do not reject

H0.

There

is

sufficient evidence at the

α=0.10

level of significance to conclude that the two groups of graduates were paid differently.

B.

Reject

H0.

There

is

sufficient evidence at the

α=0.10

level of significance to conclude that the two groups of graduates were paid differently.

C.

Do not reject

H0.

There

is not

sufficient evidence at the

α=0.10

level of significance to conclude that the two groups of graduates were paid differently.

D.

Reject

H0.

There

is not

sufficient evidence at the

α=0.10

level of significance to conclude that the two groups of graduates were paid differently.

5.

A treadmill manufacturer has developed a new machine with softer tread and better fans than its current model. The manufacturer believes these new features will enable runners to run for longer times than they can on its current machines. To determine whether the desired result is achieved, the manufacturer randomly sampled

35

runners. Each runner was measured for one week on the current machine and for one week on the new machine. The accompanying data displays weekly total number of minutes for each runner on the two types of machines. At the

0.02

level of significance, can the treadmill manufacturer conclude that the new machine has the desired result?

Click the icon to view the treadmill times.

Let

μd=μ1−μ2,

where

μ1

is the total new treadmill time and

μ2

is the total current treadmill time. Determine the null and alternative hypotheses. Choose the correct answer below.

A.

H0:

μd≠0

HA:

μd=0

B.

H0:

μd≤0

HA:

μd>0

C.

H0:

μd=0

HA:

μd≠0

D.

H0:

μd≥0

HA:

μd<0

Calculate the test statistic.

t= 1.081.08

(Round to two decimal places as needed.)

Calculate the p-value.

p-value= 0.1430.143

(Round to three decimal places as needed.)

State the conclusion. Choose the correct answer below.

A.

Reject

H0.

There is sufficient evidence that the new machine has the desired result.

B.

Do not reject

H0.

There is insufficient evidence that the new machine has the desired result.

C.

Do not reject

H0.

There is sufficient evidence that the new machine has the desired result.

D.

Reject

H0.

There is insufficient evidence that the new machine has the desired result.

Question is complete.

6.

Suppose a random sample of

90

companies taken in

2003

showed that

19

offered high-deductible health insurance plans to their workers. A separate random sample of

100

firms taken in

2004

showed that

32

offered high-deductible health insurance plans to their workers. Based on the sample results, can you conclude that there is a higher proportion of companies offering high-deductible health insurance plans to their workers in

2004

than in

2003?

Conduct your hypothesis test at a level of significance

α=0.01.

Let

p1

be the population proportion from

2004,

and let

p2

be the population proportion from

2003.

Identify the null and alternative hypotheses. Choose the correct answer below.

A.

H0:

p1−p2≠0

HA:

p1−p2=0

B.

H0:

p1−p2≤0

HA:

p1−p2>0

Your answer is correct.

C.

H0:

p1−p2<0

HA:

p1−p2≥0

D.

H0:

p1−p2=0

HA:

p1−p2≠0

E.

H0:

p1−p2>0

HA:

p1−p2≤0

F.

H0:

p1−p2≥0

HA:

p1−p2<0

Determine the critical value(s).

z Subscript alphazα

=

(Use a comma to separate answers as needed. Round to

two

decimal places as needed.)

Calculate the test statistic.

z=

Reach a decision. Choose the correct answer below.

A.

Do not reject

the null hypothesis. There is

sufficient

evidence to conclude that there is a higher proportion of companies offering high-deductible health insurance plans to their workers in

2004

than in

2003.

B.

Reject

the null hypothesis. There is

sufficient

evidence to conclude that there is a higher proportion of companies offering high-deductible health insurance plans to their workers in

2004

than in

2003.

C.

Do not reject

the null hypothesis. There is

insufficient

evidence to conclude that there is a higher proportion of companies offering high-deductible health insurance plans to their workers in

2004

than in

2003.

D.

Reject

the null hypothesis. There is

insufficient

evidence to conclude that there is a higher proportion of companies offering high-deductible health insurance plans to their workers in

2004

than in

2003.