Inferential Statistics

1.Suppose the mean life of a battery if we observed a sample size of 50 and found out that the sample mean is 40 months with a marginerror of 1.96.Identify :

Estimate = __________________

95% confidence interval = ______________________

Interpretation:___________________________________________

2.Researchers in a certain medical center are interested in assessing the effect of chronic lecithin use on total blood cholesterol.A sample of ten middle-aged men with hypercholesterolemia had their total cholesterol measured prior to and following six month period regimen of lecithin intake.The researchers would like to test whether the population mean blood cholesterol level changed significantly after prolonged lecithin used.

a.What statistical treatment is applicable to the situation?Explain.

b.State the null hypothesis.

c.If the computed statistics is 1.38 with a p value of 0.20, what is your conclusion at 95% level of confidence?

3.A company has 455 job openings: 70 for professional jobs and 385 for blue collar jobs.Below is the summary of the results of job applications of 600 men and 300 women for these new jobs.

Type of JobMenWomen

Appliedhiredappliedhired

Professional2003020040

Blue collar40030010085

a.Suggest statistical treatment to establish dependence between type of job and sex.

b.State the null hypothesis.

c.At 10 % level of significance, what will be your decision (in terms of reject and do not reject the null hypothesis) if the p value is 0.05?

d.State the conclusion.

4.Two formulations of a new whitening soap are to be compared as to their whitening effect.A random sample of 40 potential users of the soap is selected.Each person uses a randomization mechanism to determine which formulation is better as a whitening soap, the one that is applied on the left arm or the other formulation is applied on the right arm.After two weeks, they measured the effect of formulation.

a.What statistical treatment should be used to treat the data?

b.State the null hypothesis?

c.State the conclusion if the computed p value is 0.05 at 5% level of significance.

5.The principal of a school wishes to determine if the grade 6 boys are better in mathematics than the grade 6 girls.Random samples of boys were selected.Then random samples of girls were selected.All the students in the two groups were asked to take a standardized test in mathematics.

a.What variable is measured in the study?

b.How would you state the null hypothesis?

c.What statistical measure will be used in the analysis of the data?

6.The data below represent the number of hours of pain relief provided by 5 different brands of headache tablets administered to 25 subjects.The 25 subjects were randomly divided into 5 groups and each group was treated with a different brand.You would like to test if there is significant difference between the 5 brands?

TABLET BRAND

ABCDE

59327

47536

88249

66314

39747

Q1. State the null hypothesis.

Q2.Below is one of the processed data.Is the null hypothesis accepted or rejected?

ANOVA

Hours

Sum of Squares

df

Mean Square

F

Sig.

Between Groups

79.440

4

19.860

6.896

.001

Within Groups

57.600

20

2.880

Total

137.040

24

Descriptives

Hours

N

Mean

Std. Deviation

Std. Error

95% Confidence Interval for Mean

Minimum

Maximum

Lower Bound

Upper Bound

A

5

5.20

1.924

.860

2.81

7.59

3

8

B

5

7.80

1.304

.583

6.18

9.42

6

9

C

5

4.00

2.000

.894

1.52

6.48

2

7

D

5

2.80

1.304

.583

1.18

4.42

1

4

E

5

6.60

1.817

.812

4.34

8.86

4

9

Total

25

5.28

2.390

.478

4.29

6.27

1

9

Q3.It can be seen that the tablet brand B has the highest mean value?What does it imply?

Consider the Post Hoc Test on the next page for you to answer the statements following the tabulation in terms of YES or NO.

Post Hoc Tests

Multiple Comparisons

Dependent Variable: hours

LSD

(I) Tablet

(J) Tablet

Mean Difference (I-J)

Std. Error

Sig.

95% Confidence Interval

Lower Bound

Upper Bound

A

B

-2.600^*

1.073

.025

-4.84

-.36

C

1.200

1.073

.277

-1.04

3.44

D

2.400^*

1.073

.037

.16

4.64

E

-1.400

1.073

.207

-3.64

.84

B

A

2.600^*

1.073

.025

.36

4.84

C

3.800^*

1.073

.002

1.56

6.04

D

5.000^*

1.073

.000

2.76

7.24

E

1.200

1.073

.277

-1.04

3.44

C

A

-1.200

1.073

.277

-3.44

1.04

B

-3.800^*

1.073

.002

-6.04

-1.56

D

1.200

1.073

.277

-1.04

3.44

E

-2.600^*

1.073

.025

-4.84

-.36

D

A

-2.400^*

1.073

.037

-4.64

-.16

B

-5.000^*

1.073

.000

-7.24

-2.76

C

-1.200

1.073

.277

-3.44

1.04

E

-3.800^*

1.073

.002

-6.04

-1.56

E

A

1.400

1.073

.207

-.84

3.64

B

-1.200

1.073

.277

-3.44

1.04

C

2.600^*

1.073

.025

.36

4.84

D

3.800^*

1.073

.002

1.56

6.04

Q4.Answer in terms ofyesornobased on the two prior tables.

Tablet A is significantly more effective than B.___________

Tablet A is significantly more effective than C.___________

Tablet A is significantly more effective than D.___________

Tablet A is significantly more effective than E.___________

Tablet B is significantly more effective than C.___________

Tablet B is significantly more effective than D.___________

Tablet B is significantly more effective than E.___________

Tablet C is significantly more effective than D.___________

Tablet C is significantly more effective than E.___________

Tablet D is significantly more effective than E.___________

7.The ages and heart rates (beats per minute) of 20 patients who participated in a clinical trial for a new anti-hypertensive medication:

Patient No.Agesheart rates

14892

24576

36770

44472

55764

66270

75379

86292

94772

103784

113972

123670

135176

144168

154976

167076

175860

186776

195468

204976

Q1.State the null hypothesis.

Q2. What can we conclude about the relationship between age and heart rate?

Q3.Is the relationship significant at 0.05?

Descriptive Statistics

Mean

Std. Deviation

N

Age

51.80

10.217

20

Heart Rate

74.45

8.016

20

Correlations

Age

Heart Rate

Age

Pearson Correlation

1

-.039

Sig. (2-tailed)

.869

N

20

20

Heart Rate

Pearson Correlation

-.039

1

Sig. (2-tailed)

.869

N

20

20