MWATU

4. Suppose the manufacturer of Advil, a common headache remedy, recently developed a new formulation of the drug that is claimed to be more effective. To evaluate the new drug, a sample of 270 current users is asked to try it. After a one-month trial, 251 indicated the new drug was more effective in relieving a headache. At the same time a sample of 390 current Advil users is given the current drug but told it is the new formulation. From this group, 352 said it was an improvement.

(1)

State the decision rule for .01 significance level: H0: πn ≤ πc; H1: πn > πc. (Round your answer to 2 decimal places.)

  Reject H0 if z >

(2)

Compute the value of the test statistic. (Do not round the intermediate value. Round your answer to 2 decimal places.)

  Value of the test statistic

(3)

Can we conclude that the new drug is more effective? Use the .01 significance level.

   H0. We conclude that the new drug is more effective.

A study of the effect of television commercials on 12-year-old children measured their attention span, in seconds. The commercials were for clothes, food, and toys.

Clothes

Food

Toys

26

45

60

21

48

51

43

43

43

35

53

54

28

47

63

31

42

53

17

34

48

31

43

58

20

57

47

47

51

44

51

54

Click here for the Excel Data File

(1)

Complete the ANOVA table. Use .05 significance level. (Round the SS and MS values to 1 decimal place and F value to 2 decimal places. Leave no cells blank - be certain to enter "0" wherever required. Round the DF values to nearest whole number.)

  Source

DF

SS

MS

F

P

  Factors

  Error

  Total

(2)

Find the values of mean and standard deviation. (Round the mean and standard deviation values to 3 decimal places.)

  Level

N

Mean

StDev

  Clothes

  Food

  Toys

(3)

Is there a difference in the mean attention span of the children for the various commercials?

  The hypothesis of identical means can definitely be .

  There is in the mean attention span.

(4)

Are there significant differences between pairs of means?

Clothes have a mean attention span of at least ten minutes the other groups.

Given the following sample information, test the hypothesis that the treatment means are equal at the .05 significance level.

Treatment 1

Treatment 2

Treatment 3

8          

3

3

11          

2

4

10          

1

5

3

4

2

 Click here for the Excel Data File

(a-1)

State the null hypothesis and the alternate hypothesis.

      Null hypothesis

Ho: μ1 = μ2 = μ3

Ho: μ1 = μ2

Multiple Choice

Difficulty: Medium

Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.

(a-2)

Alternative hypothesis

H1: Treatment means are not all the same

H1: Treatment means are all the same

Multiple Choice

Difficulty: Medium

Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.

(b)

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

  Reject Ho if F >

Worksheet

Difficulty: Medium

Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.

(c)

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

  SST

  SSE

  SS total

Worksheet

Difficulty: Medium

Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.

(d)

Complete an ANOVA table. (Round F, SS to 2 decimal places and MS to 3 decimal places.)

  Source

SS

df

MS

F

  Treatments

  Error

  Total

Worksheet

Difficulty: Medium

Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.

(e)

State your decision regarding the null hypothesis.

Do not reject H0.

Reject H0.

Multiple Choice

Difficulty: Medium

Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results.

(f)

If H0 is rejected, can we conclude that treatment 1 and treatment 2 differ? Use the 95 percent level of confidence.

  , we conclude that the treatments 1 and 2 have different