STAT 101- define term correlation and answer the following quiz

STAT 101- define term correlation and answer the following quiz

Subject: Mathematics    / Statistics
Question

Section-I

State whether the following statements are True or False. (6 marks, 1 Mark each)

The term correlation refers to how two variables vary independently of one another.

Outliers can increase or decrease the value of r.

The linear correlation coefficient may assume any value -1 ? r ? 1.

When conducting a hypothesis test with chi-square analysis, the rejection region in a chi-square distribution is always in the upper or right tail.

ANOVA is the preferred method for finding differences among several population proportions.

If P-value £a,reject H1.

Section-II

Multiple choice questions. (6 marks, 1 Mark Each)

In goodness of fit test. If k= 25 ( number of different categories or cells) and n ( number of trials) , and then expected frequency for each cell is:
10
1.5
20
0.5

In contingency table. The corresponded degree of freedom for Chi-square in test of independence for 3×4 table is:
12
2
3
6

Analysis of variance (ANOVA) is a method for testing the hypothesis:

a. That three or more population means are equal.

b. Those at most three population means are equal.

c. That three or more population means are NOT equal.

d. That two population means are equal.

If the equation of regression is given by 9X -10Y +77 = 0, then the values of b0 ( intercept)and b1 (slope) are respectively given by :
7.7, 0.9

7.7, 0.7
0.7, 7.
0.9, 7.7

If SS (Total) and SS (error) then the value of SS (Treatment) in 1 way ANOVA is?
75
115.
85
None of the above.

A fitted linear regression model is . If x = 1 and the corresponding observed value of y = 11, the residual at this observation is:
+1
-1
0
-2

Section-III

Answer the following Essay Type Question (18 marks, 3 Mark Each)

Five pair of shoes print length and height were used to conduct a formal hypothesis test of the claim that there is linear correlation between the two variables. Use the value of r .591and find the appropriate test statistics method at 0.05 significance level. Also based on the result compare and conclude whether it is reject hypothesis or fail to reject the null hypothesis. ( P-value is 0.2937)

Given the sample data below, find the F test statistic value According to Berford’s law, a variety of different data sets includes numbers with leading (first) digits that follow the distribution shown in the nine row of Table 1. The bottom row lists the frequencies of leading digits of the populations of all 120 countries from New York and California combined. Test the claim that those 120 countries have populations with leading digits that follow Benford’s law.

Leading digit

Benford’slaw:Distibution of leading digit

CA and NY country population

1

30.1%

33

2

17.6%

22

3

12.5%

10

4

9.7%

15

5

7.9%

10

6

6.7%

9

7

5.8%

5

8

5.1%

7

9

4.6%

9

Find Linear correlation coefficient between X and Y and also obtain the Regression equation for the following data:

Hours(X)

Score(Y)

1

1

1

3

3

2

4

5

6

4

7

5

8

7

8

8

While conducting a one-way ANOVA comparing five treatments with 10 observations per treatment, computedvalue for SST = 250 and MSE = 3 given. Find the value of F and also construct the ANOVA table?

Find the expected frequency for the given Contingency Table, where the Observed frequency is 88 and 10.Use a 0.05 significance level to test the claim that getting an infection (cold) is independent of the treatment group. What does the result indicates about the effectiveness of Echinacea as a treatment for colds?

Treatment Group

Placebo

Echinacea:20%extract

Echinacea:60%extract

Infected

88

48

42

Not Infected

15

4

10