Question 3

a) A random sample of 10 observations from Population A revealed a sample mean of 23

and a sample standard deviation of 4. A random sample of 8 observations from another

population revealed a sample mean of 26 and a sample standard deviation of 5. At the

.05 significance level, is there a difference between the population means? Assume the

sample populations do not have equal standard deviations.

i. State null and alternate hypotheses. (2 marks)

ii. Compute the test statistics. (4 marks)

iii. What is your decision regarding the null hypothesis? (2 marks)

b) The following table represents x as independent variable while y as dependent

variable.

X 3.5 4 5 5.5 6 a 7.23 8.67 9.5

Y 22 23.5 24 25 b c 28.5 29.5 30.5

Assume the following regression output is obtained from the values of X and Y. Both

variables have a strong positive relationship with = 0.9860. The mean value of Y is

26.2778 and the standard deviations for X and Y values are equal to 2.01164 and

2.9059, respectively. Meanwhile, a refers to unknown value of X, and b and c signify

unknown values of Y.

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.986031

R Square 0.972258

Adjusted R

Square 0.968295

Standard

Error 0.517428

Observations 9

ANOVA

df SS MS F

Significance

F

Regression 1 65.68143 65.68143 245.3251 1.05E-06

Residual 7 1.874126 0.267732

Total 8 67.55556

Coefficients

Standard

Error t Stat P-value Lower 95%

Upper

95%

Lower

95.0%

Upper

95.0%

Intercept 17.40229 0.592325 29.37962 1.36E-08 16.00167 18.80292 16.00167 18.80292

X Variable 1 1.424382 0.09094 15.66286 1.05E-06 1.209343 1.639421 1.209343 1.6394.

i. Compute the covariance between X and Y. (2 marks)

ii. What is the value of a? (Round to 2 decimal places). (4 marks)

iii. Show with numerical values how the regression sum of squares is obtained.

(6 marks)

[Total: 20 marks]