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A sample of 36 observations is selected from a normal population. The sample mean is 12, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.01 significance level.

H0: μ ≤ 10

H1: μ > 10

a.

Is this a one- or two-tailed test?

b.

What is the decision rule?

c.

What is the value of the test statistic?

  Value of the test statistic

d.

What is your decision regarding H0?

e.

What is the p-value?

  p-value

Given the following hypotheses:

H0 : μ = 400

H1 : μ ≠ 400

A random sample of 12 observations is selected from a normal population. The sample mean was 407 and the sample standard deviation 6. Using the .01 significance level:

a.

State the decision rule. (Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.)

  Reject H0 when the test statistic is the interval (,).

b.

Compute the value of the test statistic. (Round your answer to 3 decimal places.)

  Value of the test statistic

c.

What is your decision regarding the null hypothesis?

The management of White Industries is considering a new method of assembling its golf cart. The present method requires 42.3 minutes, on the average, to assemble a cart. The mean assembly time for a random sample of 24 carts, using the new method, was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes. Using the .10 level of significance, can we conclude that the assembly time using the new method is faster?

a.

What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

  Reject H0 : μ ≥ 42.3 when the test statistic is  .

b.

Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

  Value of the test statistic

c.

What is your decision regarding H0?

Given the following hypotheses:

H0 : μ = 100

H1 : μ ≠ 100

A random sample of six resulted in the following values: 118, 105, 112, 119, 105, and 111. Assume a normal population.

a.

Using the .05 significance level, determine the decision rule? (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

  Reject H0 : μ = 100 when the test statistic is (,   ).  

b.

Compute the value of the test statistic. (Round your answer to 2 decimal places.)

  Value of the test statistic

C-1.

What is your decision regarding the H0?

C-2.

Can we conclude the mean is different from 100?

d.

Estimate the p-value.

  The p-value is    

A sample of 65 observations is selected from one population with a population standard deviation of 0.75. The sample mean is 2.67. A sample of 50 observations is selected from a second population with a population standard deviation of 0.66. The sample mean is 2.59. Conduct the following test of hypothesis using the .08 significance level.

H0 : μ1 ≤ μ2

H1 : μ1 > μ2

a.

This a -tailed test.

b.

State the decision rule. (Negative values should be indicated by a minus sign. Round your answer to 2 decimal places.)

  The decision rule is to reject H0 if z is  .

c.

Compute the value of the test statistic. (Round your answer to 2 decimal places.)

  Value of the test statistic

d.

What is your decision regarding H0?

H0.

e.

What is the p-value? (Round your answer to 4 decimal places.)

  p-value

The null and alternate hypotheses are:

A random sample of 15 observations from the first population revealed a sample mean of 350 and a sample standard deviation of 12. A random sample of 17 observations from the second population revealed a sample mean of 342 and a sample standard deviation of 15.

At the .10 significance level, is there a difference in the population means?

a.

This is a -tailed test.

b.

The decision rule is to reject if or . (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

c.

The test statistic is t =. (Round your answer to 3 decimal places.)

d.

What is your decision regarding?

e.

The p-value is.

The null and alternate hypotheses are:

H0: μ1 ≤ μ2

H1: μ1 > μ2

A random sample of 20 items from the first population showed a mean of 100 and a standard deviation of 15. A sample of 16 items for the second population showed a mean of 94 and a standard deviation of 8. Use the .05 significant level.

a.

Find the degrees of freedom for unequal variance test. (Round down your answer to the nearest whole number.)

  Degrees of freedom

b.

State the decision rule for .05 significance level. (Round your answer to 3 decimal places.)

  Reject H0 if t>.

c.

Compute the value of the test statistic. (Round your answer to 3 decimal places.)

  Value of the test statistic

d.

What is your decision regarding the null hypothesis? Use the .05 significance level.

  The null hypothesis is.

The following are six observations collected from treatment 1, four observations collected from treatment 2, and five observations collected from treatment 3. Test the hypothesis at the 0.05 significance level that the treatment means are equal.

Treatment 1

Treatment 2

Treatment 3

9

13

10

7

20

9

11

14

15

9

13

14

12

15

10

a.

State the null and the alternate hypothesis.

Ho : μ1 μ2   μ3

H1 :  Treatment means all the same.

b.

What is the decision rule? (Round your answer to 2 decimal places.)

  Reject Ho if F >

c.

Compute SST, SSE, and SS total. (Round your answers to 2 decimal places.)

 SST =   

 SSE =   

 SS total =   

d.

Complete the ANOVA table. (Round SS, MS and F values to 2 decimal places.)

Source

SS

df

MS

F

Treatments

Error

6.88   

Total

152.93   

e.

State your decision regarding the null hypothesis.

Decision: Ho  

A stock analyst wants to determine whether there is a difference in the mean rate of return for three types of stock: utility, retail, and banking stocks. The following output is obtained:

We are studying mutual bond funds for the purpose of investing in several funds. For this particular study, we want to focus on the assets of a fund and its five-year performance. The question is: Can the five-year rate of return be estimated based on the assets of the fund? Nine mutual funds were selected at random, and their assets and rates of return are shown below.

Assets

Return

Assets

Return

  Fund

($ millions)

(%)

  Fund

($ millions)

(%)

  AARP High Quality Bond

$622.2

10.8

  MFS Bond A

$494.5

11.6

  Babson Bond L

160.4

11.3

  Nichols Income

158.3

9.5

  Compass Capital Fixed Income

275.7

11.4

  T. Rowe Price Short-term

681.0

8.2

  Galaxy Bond Retail

433.2

9.1

  Thompson Income B

241.3

6.8

  Keystone Custodian B-1

437.9

9.2

b-1.

Compute the coefficient of correlation. (Round your answer to 3 decimal places. Negative amount should be indicated by a minus sign.)

r  =  

b-2.

Compute the coefficient of determination. (Round your answer to 3 decimal places.)

r2 =

c.

Give a description of the degree of association between the variables.

There is  association between the variables.

d.

Determine the regression equation. Use assets as the independent variable. (Round your answers to 4 decimal places. Negative amounts should be indicated by a minus sign.)

b =  

a =  

e.

For a fund with $400.0 million in sales, determine the five-year rate of return (in percent). (Round your answer to 4 decimal places.)

=  The equation should be used with caution. Assets do not account for much of the variation in the rate of return.

On the first statistics exam, the coefficient of determination between the hours studied and the grade earned was 80%. The standard error of estimate was 10. There were 20 students in the class. Develop an ANOVA table for the regression analysis of hours studied as a predictor of the grade earned on the first statistics exam.

  Source

DF

SS

MS

  Regression

  Error

  Total