Question

Q: A 95% confidence interval for the mean is (102, 106). If we test Ho: ? = 100 vs. H1: ? ?
100, the p-value will be:
(A) larger than 0.05
(B) smaller than 0.05
(C) larger than 0.01
(D) smaller than 0.01

Q: Suppose you want to conduct a t-test using ? = 0.05. You take a random sample of size 30
and obtain the sample mean and sample standard deviation. As a result, you fail to reject the null
hypothesis and its p-value is 0.07. Now, you decide to take a random sample with size 40 from
the same population and you obtain the same sample mean and sample standard deviation.
Compared with the p-value for n = 30, the p-value for n = 40 will:

(A) be smaller
(B) be larger
(C) stay the same
(D) be either smaller or larger depending on the ? error

Q:

The weight (X) and systolic blood pressure (Y) of 50 randomly selected males in the age
group between 25 and 30 are obtained and you obtained the following fitted regression line:
y = 69.1+.42x

One of the 50 people weighs 200 pounds with a systolic blood pressure of 128 mmHg. What is

the residual for this person?

Q: Given a certain set of the data, you obtained the values of the correlation coefficient and the
coefficient of determination. You then quickly realized that you should’ve swapped the
independent variable (X) and the response variable (Y). If you swap X and Y, what is your
expectation?
(A) The value of the correlation coefficient may change, but the value of the coefficient of
determination will not change
(B) The value of the coefficient of determination may change, but the value of the correlation
coefficient will not change
(C) Both values will change
(D) None of the values will change

Answer 1

Q1) Given Mean - Marginal Error = 102
Mean + Marginal Error = 106
thus, 2 Mean = 102+106
mean = 104
Therefore, Marginal Error = 106-104 = 2
1.96 * SD/sqrt(n) = 2
SD / sqrt(n) = 2/1.96 = 1.02041
Test Statistic
Z = (104 - 100) / 1.02041 = 3.92
P-value = 0.00008

Correct answer: Option (D) samller than 0.01

Q2) Correct answer: Option (A) be smaller
since
As n increase, the SE decrease, the test statistic increase, p-value decrease

Q3)
Given X = 200
y = 69.1+0.42(200) = 153.1
Residual of this person is 128 - 153.1 = -25.1

Q4) Correct answer: (D) None of the values will change
since r_xy = r_yx