Free Printable DATA ANALYTICS (T1)

1.

Following information from ANOVA table is given to you. Using this information calculate the F-ratio: Total degree of freedom of Between and Within is 11, Total Sum of Squares of Between and Within sample is 21.4, Sum of Squares of Within sample is 2.7, Mean of Squares of Within sample is 0.31

a)

30.16

b)

32.45

c)

19.45

d)

28.79

2.

Following information from ANOVA table is given to you. Using this information calculate the F-ratio: Degree of freedom for Between sample is 3, Total degree of freedom of Between and Within is 29, Total Sum of Squares of Between and Within sample is 57, Sum of Squares of Within sample is 35

a)

4.45

b)

5.45

c)

6.45

d)

5.01

3.

To find the attitude of people on the issue of reservation for backward classes, 100 people were interviewed in Delhi, Mumbai, Kolkata & Chennai.The data obtained in favor of it are as follows: Delhi-25, Mumbai-20, Kolkata-30, Chennai-35. Calculate Chi Square calculated

a)

11.25

b)

1.25

c)

17.25

d)

4.25

4.

A pre post study gave the following results: Pre-study- 4,4,5,4.6. Its corresponding Post study values are - 3.5,4.5,4,3.9. What is the sum of Positive ranks

a)

1.5

b)

7

c)

8

d)

8.5

5.

We want to conduct a Mann Whitney test on the IQ of girls and boys. A sample of 5 boys and 6girls was selected. There details are as follows: Boys- 112,113,116,112,121. Girls - 112, 115, 116, 121, 124, 118. Find sum of ranks of Girls

a)

42

b)

24

c)

22

d)

44

6.

We want to conduct a Mann Whitney test on the IQ of girls and boys. A sample of 5 boys and 6girls was selected. There details are as follows: Boys- 112,113,116,112,121. Girls - 112, 115, 116, 121, 124, 118. Find sum of ranks of Boys

a)

42

b)

24

c)

22

d)

44

7.

Two students compared two brands of chips, Frito Lays and Golden Flakes, to see which company gives you more for your money. Five bags of each brand were measured with a very accurate scale. Use the Mann Whitney test to see if there are any significant differences between the two brands in the amount of product they put in their bags. Frito Lays: 35.3,35.4,35.8 35.9,35.9. Golden Flake: 35.3, 37.8, 38.8, 38.1, 42.5. The bags that contained 35.9 grams will receive a rank of:

a)

4

b)

4.5

c)

5

d)

5.5

8.

Two students compared two brands of chips, Frito Lays and Golden Flakes, to see which company gives you more for your money. Five bags of each brand (which, according to the label, each contained 35.4 grams) were measured with a very accurate scale. Use the Mann Whitney test to see if there are any significant differences between the two brands in the amount of product they put in their bags. What can be the alternate hypothesis?

a)

Frito Lays gives you more chips than Golden Flakes

b)

Frito Lays gives you less chips than Golden Flakes

c)

Frito Lays gives you either more or less chips than Golden Flakes

9.

Three brands of coffee are rated for taste on a scale of 1 to 10. Six persons are asked to rate each brand so that there is a total of 18 observations. The appropriate test to determine if three brand taste equally good is

a)

Mann Whitney

b)

Kruskal Wallis

c)

Wilcoxon

d)

Friedman's test

10.

In one of your experiment you counted 1600 seeds, and observed 404 as yellow and rounded, 420 as yellow and wrinkled, 400 green and round, 376 green and wrinkled. Could it be that seed colour and shape outcome are equal likely at 5% level of significance. What is the value of chi square calculated?

a)

2.56

b)

2.35

c)

2.48

d)

3.15

11.

The number of degrees of freedom in a Chi square table with 3 rows and 4 columns are

a)

12

b)

6

c)

7

d)

3

12.

In order to perform ANOVA, three sample data was collected. Sample 1 - Mean=4, n=20; Sample2- Mean=8, n=10; Sample 3 - Mean=9, n=5. Find the value of grand Mean, MS(Between)

a)

5.86, 105

b)

6.67, 210

c)

7.25, 210

d)

7.00, 105

13.

To determine whether the test statistic of ANOVA is statistically significant, it can be compared to a critical value. What two pieces of information are needed to determine the critical value?

a)

MS(between), MS(within)

b)

mean, sample standard deviation

c)

expected frequency, obtained frequency

d)

sample size, number of groups

14.

The hypothesis in an analysis of variance gets rejected if

a)

MS between groups is significantly greater than MS within group

b)

MS within group is significantly greater than MS between groups

c)

MS within group is equal to MS between groups

d)

None of the above

15.

Higher the value of computed t statistic,

a)

Larger would be the size of sample.

b)

Greater would be the probability of rejecting the null hypothesis.

c)

Greater would be the probability of accepting the null hypothesis.

d)

None of the above

16.

Two random samples have been selected and a two sample z‐test for the difference in population means is conducted with H 0: μ1 = μ2 vs. H a: μ1 ≠ μ2. The results are σ1 = 1.4, x1= 6.8, n1 = 40, σ2 = 1.6,x2= 7 , and n2 = 44. The standard error of the sampling distribution is

a)

-0.749

b)

-0.611

c)

-0.431

d)

-0.462

17.

Two random samples have been selected and a two sample z‐test for the difference in population means is conducted with H 0: μ1 = μ2 vs. H a: μ1 ≠ μ2. The results are σ1 = 1.4, x1= 6.8, n1 = 40, σ2 = 1.6,x2= 7 , and n2 = 44. The standard error of the sampling distribution is

a)

0.267

b)

0.327

c)

0.462

d)

0.107

18.

muscle strength was measured on the right and left hands of a random sample of 15 left-handed men and the difference (left - right) was found. The alternative hypothesis is one-sided (left hand stronger). The resulting t-statistic was 1.80.

a)

Df = 14, the null hypothesis can be rejected.

b)

Df = 14, the null hypothesis cannot be rejected.

c)

Df = 28, the null hypothesis can be rejected.

d)

Df = 28, the null hypothesis cannot be rejected.

19.

Which of the following is NOT true about the standard error of a statistic?

a)

The standard error increases as the sample size(s) increases.

b)

The standard error can never be a negative number.

c)

The standard error is the estimated standard deviation of the sample distribution

20.

Assume the cholesterol levels in a certain population have mean µ= 200 and standard deviation σ = 24. The cholesterol levels for a random sample of n = 9 individuals are measured and the sample mean is determined. What is the z-score for a sample mean = 180?

a)

-3.75

b)

-2.5

c)

-0.83

d)

2.5

21.

Assume the cholesterol levels in a certain population have mean µ= 200 and standard deviation σ = 24. The cholesterol levels for a random sample of n = 9 individuals are measured and the sample mean is determined. What is the z-score for a sample mean = 180?

a)

-3.75

b)

-2.5

c)

-0.83

d)

2.5

22.

The critical value of z for a two tail 90% confidence interval is

a)

1.29

b)

1.65

c)

1.96

d)

2.33

23.

A test is conducted for H 0: μ = 20, with σ = 4. A sample of size 36 has a mean of 21.40. The test statistic is

a)

0.35

b)

2.1

c)

12.6

24.

When the null hypothesis has been true, but the sample information has resulted in the rejection of the null, a _________ has been made.

a)

Level of significance

b)

Type I error

c)

Type II error

d)

Critical Value

25.

The maximum probability of a Type I error that the decision maker will tolerate is called the

a)

Level of Significance

b)

Critical value

c)

Decision value

d)

Probability Value

26.

A Type II error is the error of

a)

accepting Ho when it is false

b)

accepting Ho when it is true

c)

rejecting Ho when it is false

d)

rejecting Ho when it is true

27.

Test of hypothesis Ho: µ = 20 against H1: µ < 20 leads to:

a)

Right one-sided test

b)

Left one-sided test

c)

Two-sided test

d)

All of the above

28.

Level of significance α lies between:

a)

-1 and +1

b)

0 and 1

c)

0 and n

d)

-∞ to +∞

29.

The purpose of statistical inference is:

a)

To collect sample data and use them to formulate hypotheses about a population

b)

To draw conclusion about populations and then collect sample data to support the conclusions

c)

To draw conclusions about populations from sample data

d)

To draw conclusions about the known value of population parameter

30.

Match these parametric and non parametric

a) ANOVA (dependent samples) b) ANOVA (Independent Samples) c) Independent sample T- Test d) Paired T Test

1) Wilcoxon 2) Kruskal Wallis 3) Friedman 4) Mann Whitney

a)

a-1, b-2, c-3, d-4

b)

a-2, b-4, c-1, d-3

c)

a-3, b-2, c-4, d-1

d)

a-4, b-3, c-2, d-1

DATA ANALYTICS (T1)

Total questions: 30

Worksheet time: 3hrs 32mins

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