Question 1

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.
If the level of signiﬁcance is 0.10, what is the critical value?
A) 1.65
B) 2.58
C) 1.28
D) ±1.28
E) ±1.645

Accepted Answer

±1.645

Question 2

A manufacturer wants to increase the absorption capacity of a sponge. Based on past data, the
Average sponge could absorb 103.5ml. After the redesign, the absorption amounts of a sample of
Sponges were (in millilitres): 121.3, 109.2, 97.6, 103.5, 112.4, 115.3, 106.5, 112.4, 118.3, and 115.3. What is
The decision rule at the 0.01 level of signiﬁcance to test if the new design increased the absorption
Amount of the sponge?
A) Do not reject null hypothesis if computed t is less than 2.580
B) Do not reject null hypothesis if computed t is less than 2.821
C) Reject null hypothesis if computed z is 1.96 or larger
D) Reject null hypothesis if computed t is less than 2.764

Accepted Answer

Do reject null hypothesis if computed t is less than 2.821

Question 3

Which of the following is a test statistic used to test a hypothesis about a population?
A) α
B) β
C) μ
D) z

Accepted Answer

z

Question 4

A machine is set to ﬁll the small size packages of Smarties candies with 56 candies per bag. A
Sample revealed: 3 bags of 56, 2 bags of 57, 1 bag of 55, and 2 bags of 58. How many degrees of
Freedom are there?
A) 9
B) 1
C) 8
D) 7

Accepted Answer

7

Question 5

A manufacturer claims that less than 1% of all his products do not meet the minimum government
Standards. A survey of 500 products revealed ten did not meet the standard. If the z-statistic is
-2)58 and the level of signiﬁcance is 0.02, what is your decision?
A) You reject the null hypothesis, and agree that less than 1% fail to meet government standards.
B) You have insuﬃcient evidence to reject the null hypothesis.
C) You reject the alternate hypothesis and agree that less than 1% meet government standards.
D) You should have used the t-test.

Accepted Answer

You reject the null hypothesis, and agree that less than 1% fail to meet government

Question 6

What is the critical z-value for a one-tailed lower test at the 1% level of risk?
A) +2.58
B) -2.58
C) +2.33
D) -2.33

Accepted Answer

-2.33

Question 7

For a two-tailed test at the 0.05 signiﬁcance level, what is the rejection region when the population
Standard deviation is known?
A) Between ±1.96
B) Between ±1.65
C) Greater than +1.96 and less than -1.96
D) Greater than +1.65 and less than -1.65

Accepted Answer

Greater than +1.96 and less than -1.96

Question 8

To conduct a test of hypothesis with a small sample, we need to be able to make the following
Assumption that:
A) a larger computed value of t will be needed to reject the null hypothesis.
B) the region of acceptance will be wider than for large samples.
C) the conﬁdence interval will be wider than for large samples.
D) the population is normally distributed.

Accepted Answer

the population is normally distributed.

Question 9

If the 1% level of signiﬁcance is used and the computed value of z is +6.00, what is our decision?
A) Do not reject H0
B) Reject H0
C) Reject H1

Accepted Answer

Reject H0

Question 10

A manufacturer claims that less than 1% of all his products do not meet the minimum government
Standards. A survey of 500 products revealed ten did not meet the standard.
If the z-statistic is -2.054 and the level of signiﬁcance is 0.03, what is your decision?
A) You reject the null hypothesis, and agree that less than 1% fail to meet government standards.
B) You have insuﬃcient evidence to reject the null hypothesis.
C) You reject the alternate hypothesis and agree that less than 1% meet government standards.
D) You should have used the t-test.

Accepted Answer

You reject the null hypothesis, and agree that less than 1% fail to meet government

Question 11

A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the
Average shelf life of the mix is 216 days. After a revised mix has been developed, a sample of nine
Boxes of cake mix gave these shelf lives (in days): 215, 217, 218, 219, 216, 217, 217, 218 and 218. At the
0)025 level, has the shelf life of the cake mix increased?
A) Yes, because computed t is greater than the critical value.
B) Yes, because computed t is less than the critical value.
C) No, because computed t lies in the region of acceptance.
D) No, because 217.24 is quite close to 216.

Accepted Answer

Yes, because computed t is greater than the critical value.

Question 12

What is the critical value for t in a one-tailed hypothesis test in which a null hypothesis is tested at
The 5% level of signiﬁcance based on a sample size of 15?
A) 1.708
B) 1.711
C) 1.761
D) 2.145

Accepted Answer

1.761

Question 13

A manufacturer claims that less than 1% of all his products do not meet the minimum government
Standards. A survey of 500 products revealed ten did not meet the standard.
If the computed value of z = -2.25 and the level of signiﬁcance is 0.03, what is your decision?
A) You reject the null hypothesis, and agree that less than 1% fail to meet government standards.
B) You have insuﬃcient evidence to reject the null hypothesis.
C) You reject the alternate hypothesis and agree that less than 1% meet government standards.
D) You should have used the t-test.

Accepted Answer

You reject the null hypothesis, and agree that less than 1% fail to meet government

Question 14

What does z equal for an α = 0.01 and a lower level test?
A) +2.33
B) -2.33
C) +2.58
D) -2.58

Accepted Answer

-2.33

Question 15

A manufacturer of stereo equipment introduces new models in the fall. Retail dealers are surveyed
Immediately after the Christmas selling season regarding their stock on hand of each piece of
Equipment. It has been discovered that unless 40% of the new equipment ordered by the retailers
In the fall had been sold by Christmas, immediate production cutbacks are needed. The
Manufacturer has found that contacting all of the dealers after Christmas by mail is frustrating as
Many of them never respond. This year 80 dealers were selected at random and telephoned
Regarding a new receiver. It was discovered that 38% of those receivers had been sold. Since 38%
Is less than 40%, does this mean that immediate production cutbacks are needed or can this
Difference of 2 percentage points be attributed to sampling? Test at the 0.05 level.
Computed z = -0.37.
A) Cut back production
B) Do not cut back production
C) Cannot determine based on information given

Accepted Answer

Do cut back production

Question 16

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.
If the level of signiﬁcance is 0.10, what is the decision rule?
A) Do not reject the null hypothesis if computed z lies between -1.65 and +1.65; otherwise, reject it.
B) Do not reject the null hypothesis if computed z is greater than 1.65; otherwise, reject it.
C) Do not reject the null hypothesis if computed z lies between -1.96 and +1.96; otherwise, reject it.
D) Reject the null hypothesis if computed z is below -1.96; otherwise, reject it.

Accepted Answer

Do reject the null hypothesis if computed z lies between -1.65 and +1.65; otherwise,

Question 17

If α = 0.05 for a two-tailed test, how large is the acceptance area?
A) 0.050
B) 0.025
C) 0.950
D) 0.975

Accepted Answer

0.950

Question 18

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 19

For a one-tailed hypothesis test, the critical z-value of the test statistic is -2.33. Which of the
Following is true about the hypothesis test?
A) α = 0.05 for a lower-tailed test
B) α = 0.01 for a lower-tailed test
C) α = 0.05 for an upper-tailed test
D) α = 0.01 for an upper-tailed test

Accepted Answer

α = 0.01 for a lower-tailed test

Question 20

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.
Given the following printout, what can you determine? 
A) The alternate hypothesis is μ ≤ 2
B) You should accept the null hypothesis at the 0.05 level of signiﬁcance.
C) There is less than a 1% chance of getting these results if the null hypothesis is true, so you have very strong evidence to suggest that the average number of study hours is different
From 2.
D) You should reject the null hypothesis at the 0.05 level of signiﬁcance, but accept it when testing at the 0.01 level of signiﬁcance.
E) You should accept the null hypothesis at the 0.05 level of signiﬁcance, but reject it when testing at the 0.01 level of signiﬁcance.

Accepted Answer

There is less than a 1% chance of getting these results if the null hypothesis is true, so you

Quiz 9: Estimation and Confidence Intervals

Which of the following is a test statistic used to test a hypothesis about a population?

A machine is set to ﬁll the small size packages of Smarties candies with 56 candies per bag. A Sample revealed: 3 bags of 56, 2 bags of 57, 1 bag of 55, and 2 bags of 58. How many degrees of Freedom are there?

A manufacturer claims that less than 1% of all his products do not meet the minimum government Standards. A survey of 500 products revealed ten did not meet the standard. If the z-statistic is -2) 58 and the level of signiﬁcance is 0.02, what is your decision?

What is the critical z-value for a one-tailed lower test at the 1% level of risk?

For a two-tailed test at the 0.05 signiﬁcance level, what is the rejection region when the population Standard deviation is known?

To conduct a test of hypothesis with a small sample, we need to be able to make the following Assumption that:

If the 1% level of signiﬁcance is used and the computed value of z is +6.00, what is our decision?

A manufacturer claims that less than 1% of all his products do not meet the minimum government Standards. A survey of 500 products revealed ten did not meet the standard. If the z-statistic is -2.054 and the level of signiﬁcance is 0.03, what is your decision?

What is the critical value for t in a one-tailed hypothesis test in which a null hypothesis is tested at The 5% level of signiﬁcance based on a sample size of 15?

A manufacturer claims that less than 1% of all his products do not meet the minimum government Standards. A survey of 500 products revealed ten did not meet the standard. If the computed value of z = -2.25 and the level of signiﬁcance is 0.03, what is your decision?

What does z equal for an α = 0.01 and a lower level test?

If α = 0.05 for a two-tailed test, how large is the acceptance area?

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?

For a one-tailed hypothesis test, the critical z-value of the test statistic is -2.33. Which of the Following is true about the hypothesis test?