Exam II

Question 1

Confidence interval is obtained as
Select one:
a. point estimate ± critical value
b. point estimate ± standard error
c. point estimate ± margin of error

Answer 1

c. point estimate ± margin of error

Question 2

Given the sample proportion (p ̅) and sample size, n, we wish to obtain the confidence interval estimate of the population proportion (p). The margin of error of the confidence interval estimate is obtained as
Select one:
a. z(α/2) ×√((p(bar)(1-(p(bar))))/n)
b. z(α/2) ×√((p(1-p))/n)

Answer 2

a. z(α/2) ×√((p(bar)(1-(p(bar))))/n)

Question 3

Margin of error is obtained as
Select one:
a. point estimate ± critical value
b. critical value × standard error
c. point estimate × critical value

Answer 3

b. critical value × standard error

Question 4

Suppose (1-α)=0.9. The critical value, zα/2 , is obtained in Excel using
Select one:
a. –NORM.S.INV(0.05)
b. –NORM.S.INV(0.1)
c. –NORM.S.INV(0.2)

Answer 4

a. –NORM.S.INV(0.05)

Question 5

Suppose (1-α)=0.95 and n = 20. The critical value tα/2, can be obtained in Excel using
Select one:
a. –T.INV(0.025, 19)
b. –T.INV(0.05, 19)
c. –T.INV(0.1, 19)

Answer 5

a. –T.INV(0.025, 19)

Question 6

Suppose σ=36 and sample size n = 81. What is the standard error (S.E) of x ̅?
Select one:
a. 0.45
b. 4
c. 13.5

Answer 6

b. 4

Question 7

The sample proportion, p(bar) = 0.25 and n=36. At the 99% confidence level, the margin of error is computed to be 0.05. Which one of the following represents the 99% confidence interval estimate of p?
Select one:
a. 0.25 ± 0.05
b. 0.25 ± 0.025
c. 0.25 ± 0.07

Answer 7

a. 0.25 ± 0.05

Question 8

The sample proportion, p(bar) = 0.25 and n=36. The standard error of p(bar) (rounded to two decimal places) is given by
Select one:
a. √((0.25*0.75)/36) = 0.07
b. 0.25/√36 = 0.04
c. √(0.25*0.75) = 0.43

Answer 8

a. √((0.25*0.75)/36) = 0.07

Question 9

We have n=15, x ̅=10, s=4 and (1-α)=0.99. The standard error of x ̅ (rounded to two decimal places) is
Select one:
a. 0.27
b. 1.03
c. 7.5

Answer 9

b. 1.03

Question 10

We have n=15, x(bar)=10, s=4 and (1-α)=0.99. Using Excel and after rounding to two decimal places, the critical value, tα/2, is
Select one:
a. 2.98
b. 1.76
c. 2.14

Answer 10

a. 2.98

Question 11

When one increases the confidence level (1-α), say from 0.90 to 0.95,
Select one:
a. margin of error will increase
b. the resulting confidence interval will capture the population parameter more often
c. both A and B are correct

Answer 11

c. both A and B are correct

Question 12

When the population standard deviation (σ) is known and we wish to estimate μ, the margin of error is obtained as
Select one:
a. zα/2 × s/√n
b. tα/2 × s/√n
c. zα/2 × σ/√n

Answer 12

c. zα/2 × σ/√n

Question 13

When the population standard deviation (σ) is NOT known and we wish to estimate μ, the margin of error is obtained as
Select one:
a. zα/2 × s/√n
b. tα/2 × s/√n
c. zα/2 × σ/√n

Answer 13

b. tα/2 × s/√n

Question 14

Which one of the following is a point estimator?
Select one:
a. μ
b. x (bar)
c. p

Answer 14

b. x (bar)

Question 15

We have n=15, x(bar) =10, s=4, and (1-α)=0.99. We wish to obtain the 99% confidence interval estimate of μ. What is the margin of error (rounded to two decimal places)?

Answer 15

3.07

Question 16

Given the following:
D:  μ≥1000; 
E:  μ<1000
D and E represent respectively.
Select one:
a. H(a) and H(0)
b. H(0) and H(a)
c. Type I error and Type II error

Answer 16

b. H(0) and H(a)

Question 17

The value 1000 in question 1) above represents
Select one:
a. H(0)
b. H(a)
c. Hypothesized value

Answer 17

c. Hypothesized value

Question 18

In hypothesis testing, the level of significance, α, represents
Select one:
a. The probability of making Type II error
b. The probability of making Type I error
c. The hypothesized value

Answer 18

b. The probability of making Type I error

Question 19

An error that occurs when we fail to reject H(0) while false is called
Select one:
a. Type I error
b. Type II error
c. α

Answer 19

b. Type II error

Question 20

Which one of the following cannot be an alternative hypothesis H(a)?
Select one:
a. p > 0.3
b. p ≥ 0.3
c. p < 0.3
d. p ≠ 0.3

Answer 20

b. p ≥ 0.3

Question 21

Questions 6 to 10 are related.  Based on a random sample of n=15 observations, we have obtained a sample mean of x(bar)=1050. The goal is to test:
H(0):  μ≤1000 and
H(a):   μ>1000 
Assume that x is normally distributed with σ=150. What is the standard error (σ (x bar) )? Rounded to two decimal places.
Select one:
a. 150/15 = 10
b. 150/√15 = 38.73
c. None of the above

Answer 21

b. 150/√15 = 38.73

Question 22

To conduct the test as given in question 6), which test statistics, is appropriate?
Select one:
a. t
b. z
c. F
d. None of the above

Answer 22

b. z

Question 23

Building on question 7), what is the value of the test statistics? Rounded to two decimal places.
Select one:
a. (1050-1000)/38.73 = 1.29
b. (1050-1000)/10 = 5
c. None of the above

Answer 23

a. (1050-1000)/38.73 = 1.29

Question 24

Using α=0.1, what is the critical value (use Excel) for testing the hypotheses in question 6)? Rounded to two decimal places.
Select one:
a. –T.INV(0.1, 14) = 1.35
b. –NORM.S.INV(0.1) = 1.28
c. –T.INV(0.05, 14) = 1.76
d. -NORM.S.INV(0.05) = 1.64

Answer 24

b. –NORM.S.INV(0.1) = 1.28

Question 25

Using correct answers for questions 8) and 9), Select one: a. We reject H(0) because the test statistics value is less than the critical value b. None of the above is correct c. We reject H(0) because the test statistics value is greater than the critical value

Answer 25

c. We reject H(0) because the test statistics value is greater than the critical value

Question 26

``` Question 11-14 are related. Based on the random sample of n=800 observations, we have obtained a sample proportion p(bar) =0.44. The goal is to test: H(0): p≥0.48 H(a): p<0.48 What is the standard error (σ(p))? Rounded to four decimal places. Select one: a. (0.48*0.52)/800 = 0.0003 b. √((0.48*0.52)/800) = 0.0177 c. None of the above ```

Answer 26

b. √((0.48*0.52)/800) = 0.0177

Question 27

``` What is the value of the test statistics? Rounded to two decimal places. Select one: a. z=(0.44-0.48)/0.0003 = -133.33 b. z=(0.44-0.48)/0.0177 = -2.26 c. None of the above ```

Answer 27

b. z=(0.44-0.48)/0.0177 = -2.26

Question 28

``` Using α=0.05, what is the critical value (use Excel) for testing the hypotheses in question 11)? Rounded to two decimal places. Select one: a. –NORM.S.INV (0.05) =1.64 b. NORM.S.INV (0.05) = -1.64 c. –NORM.S.INV(0.025) = 1.96 d. NORM.S.INV(0.025) = -1.96 ```

Answer 28

b. NORM.S.INV (0.05) = -1.64

Question 29

Using correct answers for questions 12) and 13), Select one: a. We reject H(0)because z is greater than the critical value b. We reject H(0)because z is less than the critical value c. None of the above is correct

Answer 29

b. We reject H(0)because z is less than the critical value