Statistics Assignment 4 with Solutions and Answers

Assignment NO. 4
STATISTICS (STAT-101)
Answer all the Questions on the same question paper.
Section-I
State whether the following statements are True or False.
1. The hypothesis that an analyst is trying to prove is called the alternative hypothesis.
TRUE
2. One-way ANOVA is used when analyzing the difference between more than two
population means. TRUE
3. If r = 0.9, then r 2 = 0.81, which means that 19% of the total variation in y remains
unexplained. TRUE
4. The chi-square goodness-of-fit test cannot be used to test for normality. FALSE
5. If x and y have a strong positive linear correlation, r is close to 0. FALSE
6. A test of independence CHI-SQUARE tests the null hypothesis that in a contingency
table, the row and column variables are independent. TRUE
Section-II
Multiple choice questions.
1. Which of the following is true of the null and alternative hypotheses?
a. Exactly one hypothesis must be true - TRUE
b. both hypotheses must be true
c. It is possible for both hypotheses to be true
d. It is possible for neither hypothesis to be true
2. The form of the alternative hypothesis can be:
a. one-tailed
b. two-tailed
c. neither one nor two-tailed
d. one or two-tailed - TRUE
3. The value set for is known as:
a. the rejection level
b. the acceptance level

c. the significance level - TRUE
d. the error in the hypothesis test
4. The ANOVA test is based on which assumptions?
I. the sample are randomly selected
II. the population variances are all equal to some common variance
III. the populations are normally distributed
IV. the populations are statistically significant
a. All of the above
b. II and III only
c. I, II, and III only
d. I, and III only
5. The variance within samples (S2p) for the variances 4, 2, and 6 is equal to:
a. 4
b. 5
c. 6
d. None -TRUE
6. A regression between foot length (response variable in cm) and height (explanatory
variable in inches) for 33 students resulted in the following regression equation: yˆ =
10.9 + 0.23 x. One student in the sample was 73 inches tall then the predicted foot
length for this student is. [y^ = 10.9 + 0.23 *(73)]
a. 17.57 cm
b. 27.69 cm - TRUE
c. 29 cm
d. 33 cm
Page 2 of 7

Section-III
Answer the following Essay Type Question
1. The time x in years that an employee spent at a company and the employee’s hourly pay,
y, for 5 employees are listed in the table below.
A-Calculate and interpret the correlation coefficient r.
B-Find the Regression equation. Include a plot of the data in your discussion.
X Y
5 25
3 20
4 21
10 35
15 38
A. Solution:
Correlation coefficient [r ]= 1
n−1 [ ∑ ∑ ( x−xmean )∗( y− ymean)
s x∗s y ]
n=5
Mean of X= 5+3+4 +10+15
5 =7.4
Mean of Y =25+ 20+21+35+38
5 =27.8
X Y X-X_mean Y-Y_mean Squared X
deviations
Squared Y
deviations
(X-X_mean) * (Y-
Y_mean)
5 25 -2.4 -2.8 5.76 7.84 6.72
3 20 -4.4 -7.8 19.36 60.84 34.32
4 21 -3.4 -6.8 11.56 46.24 23.12
10 35 2.6 7.2 6.76 51.84 18.72
15 38 7.6 10.2 57.76 104.04 77.52
7.4 27.8 SUM 101.2 270.8 160.4
Standard deviation of X (sX )= √ ∑ ( X− Xmean )2
5−1
¿ √ 101.2
4 =5.03
Standard deviation of Y (sY )= √ ∑ ( Y −Y mean )2
5−1
¿ √ 270.8
4 =8.23
Correlation ( r )= 1
4 [ 160.4
5.03∗8.23 ] Page 3 of 7