Question 1

It is claimed that in a bushel of peaches less than ten percent are defective. A sample of 400
Peaches is examined and 50 are found to be defective. What is the alternate hypothesis for a one-
Sided test?
A) p ≠ 0.10
B) p > 0.10
C) p ≤ 0.10
D) p = 0.10
E) p < 0.10

Accepted Answer

p < 0.10

Question 2

A nationwide survey of college students was conducted and found that students spend two hours
Per class hour studying. A professor at your school wants to determine whether the time students
Spend at your school is signiﬁcantly different from the two hours. A random sample of ﬁfteen
Statistics students is carried out and the ﬁndings indicate an average of 1.75 hours with a standard
Deviation of 0.24 hours.
A) H0 is μ ≠ 2. H1 is μ = 2.
B) H0 is μ = 2. H1 is μ ≠ 2.
C) H0 is μ = 2. H1 is μ > 2.
D) H0 is μ = 2. H1 is μ < 2.
E) H0 is μ ≠ 2. H1 is μ > 2.

Accepted Answer

H0 is μ = 2. H1 is μ ≠ 2.

Question 3

The mean gross annual incomes of certiﬁed tack welders are normally distributed with the mean of
$50,000 and a standard deviation of $4,000. The ship building association wishes to ﬁnd out
Whether their tack welders earn more or less than $50,000 annually. The alternate hypothesis is
That the mean is not $50,000.
Which of the following is the alternate hypothesis?
A) p ≠ $50,000
B) μ ≠ $50,000
C) μ < $50,000
D) μ = $50,000
E) p = $50,000

Accepted Answer

μ ≠ $50,000

Question 4

From past records it is known that the average life of a battery used in a digital clock is 305 days.
The battery life is normally distributed. The battery was recently modiﬁed to last longer. A sample of
20 of the modiﬁed batteries was tested. It was discovered that the mean life was 311 days and the
Sample standard deviation was 12 days. We want to test at the 0.05 level of signiﬁcance whether
The modiﬁcation increases the life of the battery. What is our decision rule?
A) Do not reject the null hypothesis if computed t is 1.96 or greater
B) Reject the null hypothesis if computed t is less than 1.96
C) Do not reject the null hypothesis if computed t is 1.729 or greater
D) Reject the null hypothesis if computed t is 2.086 or greater
E) Reject the null hypothesis if the computed t is 1.729 or greater

Accepted Answer

Reject the null hypothesis if the computed t is 1.729 or greater

Question 5

If the alternate hypothesis states that μ does not equal 4,000, what is the rejection region for the
Hypothesis test?
A) Both tails
B) Lower or left tail
C) Upper or right tail
D) Center

Accepted Answer

Both tails

Question 6

If the alternative hypothesis states that μ > 6,700, what is the rejection region for the hypothesis
Test?
A) Both tails
B) Lower tail
C) Upper tail
D) Center

Accepted Answer

Upper tail

Question 7

A nationwide survey of college students was conducted and found that students spend two hours
Per class hour studying. A professor at your school wants to determine whether the time students
Spend at your school is signiﬁcantly different from the two hours. A random sample of ﬁfteen
Statistics students is carried out and the ﬁndings indicate an average of 1.75 hours with a standard
Deviation of 0.24 hours.
Test at the 5% level of signiﬁcance.
A) The critical value of t is -4.03. The calculated value of t is ±2.145.
B) The critical value of t is ±2.145. The calculated value of t is -4.03.
C) The critical value of t is 1.761. The calculated value of t is -4.03.
D) The critical value of t is ±1.761. The calculated value of t is -1.041.
E) The t-test should not be used. Rather, use the z-test.

Accepted Answer

The critical value of t is ±2.145. The calculated value of t is -4.03.

Question 8

A restaurant that bills its house account monthly is concerned that the average monthly bill exceeds
$200 per account. A random sample of twelve accounts is selected, resulting in a sample mean of
$220 and a standard deviation of $12. The t-test is to be conducted at the 5% level of signiﬁcance.
A) The critical value of t is +1.796. The calculated value of t is +5.77.
B) The critical value of t is -1.796. The calculated value of t is -5.77.
C) The critical value of t is +2.201. The calculated value of t is +5.77.
D) The critical value of t is +2.201. The calculated value of t is +1.40.
E) The critical value of t is +2.201. The calculated value of t is -5.77.

Accepted Answer

The critical value of t is +1.796. The calculated value of t is +5.77.

Question 9

i. If the null hypothesis is μ ≥ 200 and the alternate hypothesis states that μ is less than 200, then, a
Two-tail test is being conducted.
ii. For a one-tailed test of hypothesis, the area of rejection is only in one tail of the curve.
iii. As the sample size increases, the curve of the t-distribution approaches the standard normal
Distribution
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Accepted Answer

(ii) and (iii) are correct statements but (i).

Question 10

What are the two rejection areas in using a two-tailed test and the 0.01 level of signiﬁcance when
The population standard deviation is known?
A) Above 1.96 and below -1.96
B) Above 1.65 and below -1.65
C) Above 2.58 and below -2.58
D) Above 1.00 and below -1.00

Accepted Answer

Above 2.58 and below -2.58

Question 11

What are the critical z-values for a two-tailed hypothesis test if α = 0.01?
A) ±1.96
B) ±2.33
C) ±2.58
D) ±1.65

Accepted Answer

±2.58

Question 12

A restaurant that bills its house account monthly is concerned that the average monthly bill exceeds
$200 per account. A random sample of twelve accounts is selected, resulting in a sample mean of
$220 and a standard deviation of $12. The t-test is to be conducted at the 5% level of signiﬁcance.
The t-value is calculated to be 5.77. At the 0.01 level of signiﬁcance, what is your decision?
A) You reject the null hypothesis, and agree that the average monthly bill exceeds $200.
B) You have insuﬃcient evidence to reject the null hypothesis.
C) You reject the alternate hypothesis and agree that the average monthly bill is less than $200.
D) You should have used the z-test.

Accepted Answer

You reject the null hypothesis, and agree that the average monthly bill exceeds $200.

Question 13

What do we call the statement that determines if the null hypothesis is rejected?
A) Decision rule
B) Test statistic
C) Alternate hypothesis
D) Critical value

Accepted Answer

Decision rule

Question 14

What is the critical value for a one-tailed hypothesis test in which a null hypothesis is tested at the
5% level of signiﬁcance based on a sample size of 25 and an unknown population standard
Deviation?
A) 1.708
B) 1.711
C) 2.060
D) 2.064

Accepted Answer

1.711

Question 15

Which of the following is NOT one of the ﬁve steps in the hypothesis testing procedure?
A) Formulate a decision rule
B) State the null and alternate hypotheses
C) Select a level for β
D) Identify the test statistic

Accepted Answer

Select a level for β

Question 16

i. For a one-tailed test using the 0.05 level of signiﬁcance, the critical value for the z test is 1.645, but
For t it is 1.96.
ii. For a one-tailed test using the 0.01 level of signiﬁcance, the critical value for the z-test is 1.645, but
For t it is 1.96.
iii. For a two-tailed test using the 0.05 level of signiﬁcance the critical value for the z-test is 1.96 and
It is the same for the t-test.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Accepted Answer

(i), (ii), and (iii) are all false statements.

Question 17

Records on a ﬂeet of trucks reveal that the average life of a set of spark plugs is normally
Distributed with a mean of 35,600 kilometres. A manufacturer of spark plugs claims that its plugs
Have an average life in excess of 35,600 kilometres. The ﬂeet owner purchased 18 sets and found
That the sample average life was 37,700 kilometres, the sample standard deviation was 2415
Kilometres and the computed t = 3.677.
A) Based on these ﬁndings, there is enough evidence to accept the manufacturer's claim at the 0.05 level.
B) Based on these ﬁndings, there is NOT enough evidence to accept the manufacturer's claim at the 0.05 level.
C) Based on these ﬁndings, there is enough evidence to accept the manufacturer's claim at the 0.05 level, but NOT at the 0.01 level.
D) Based on these ﬁndings, there is NOT enough evidence to accept the manufacturer's claim at the 0.01 level.
E) Based on these ﬁndings, there in NOT enough evidence to accept the manufacturer's claim at either the 0.05 or the 0.01 level.

Accepted Answer

Based on these ﬁndings, there is enough evidence to accept the manufacturer's claim at

Question 18

The mean length of a small counter balance bar is 43 millimeters. There is concern that the
Adjustments of the machine producing the bars have changed. Test the claim at the 0.02 level that
There has been no change in the mean length. The alternate hypothesis is that there has been a
Change. Twelve bars (n = 12) were selected at random and their lengths recorded. The lengths are
(in millimeters) 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43 and 42. The mean of the sample is 41.5 and
The standard deviation 1.784. Computed t = -2.913. Has there been a statistically signiﬁcant change
In the mean length of the bars?
A) Yes, because the computed t lies in the area beyond the critical.
B) No, because the information given is not complete.
C) No, because the computed t lies in the area to the right of -2.718.

Accepted Answer

Yes, because the computed t lies in the area beyond the critical.

Question 19

A random sample of size 15 is selected from a normal population. The population standard deviation
Is unknown. Assume that a two-tailed test at the 0.10 signiﬁcance level is to be used. For what value
Of t will the null hypothesis be rejected?
A) To the left of -1.282 or to the right of 1.282
B) To the left of -1.345 or to the right of 1.345
C) To the left of -1.761 or to the right of 1.761
D) To the left of -1.645 or to the right of 1.645

Accepted Answer

To the left of -1.761 or to the right of 1.761

Question 20

A restaurant that bills its house account monthly is concerned that the average monthly bill exceeds
$200 per account. A random sample of twelve accounts is selected, resulting in a sample mean of
$220 and a standard deviation of $12. The t-test is to be conducted at the 5% level of signiﬁcance.
A) The null hypothesis is μ ≤ 200. The alternate hypothesis is μ ≤ 200.
B) The null hypothesis is μ ≤ 200. The alternate hypothesis is μ > 200.
C) The null hypothesis is μ = 200. The alternate hypothesis is μ ≠ 200.
D) The null hypothesis is μ > 200. The alternate hypothesis is μ ≤ 200
E) The null hypothesis is μ ≤ 220. The alternate hypothesis is μ > 220.

Accepted Answer

The null hypothesis is μ ≤ 200. The alternate hypothesis is μ > 200.

Quiz 9: Estimation and Confidence Intervals

It is claimed that in a bushel of peaches less than ten percent are defective. A sample of 400 Peaches is examined and 50 are found to be defective. What is the alternate hypothesis for a one- Sided test?

If the alternate hypothesis states that μ does not equal 4,000, what is the rejection region for the Hypothesis test?

If the alternative hypothesis states that μ > 6,700, what is the rejection region for the hypothesis Test?

A restaurant that bills its house account monthly is concerned that the average monthly bill exceeds $200 per account. A random sample of twelve accounts is selected, resulting in a sample mean of $220 and a standard deviation of $12. The t-test is to be conducted at the 5% level of signiﬁcance.

What are the two rejection areas in using a two-tailed test and the 0.01 level of signiﬁcance when The population standard deviation is known?

What are the critical z-values for a two-tailed hypothesis test if α = 0.01?

What do we call the statement that determines if the null hypothesis is rejected?

What is the critical value for a one-tailed hypothesis test in which a null hypothesis is tested at the 5% level of signiﬁcance based on a sample size of 25 and an unknown population standard Deviation?

Which of the following is NOT one of the ﬁve steps in the hypothesis testing procedure?

A random sample of size 15 is selected from a normal population. The population standard deviation Is unknown. Assume that a two-tailed test at the 0.10 signiﬁcance level is to be used. For what value Of t will the null hypothesis be rejected?

A restaurant that bills its house account monthly is concerned that the average monthly bill exceeds $200 per account. A random sample of twelve accounts is selected, resulting in a sample mean of $220 and a standard deviation of $12. The t-test is to be conducted at the 5% level of signiﬁcance.