stat hw due in 10 hours
attached stat hw
2 0 2 0 M c G r a w – H i l l E d u c a t i o n . A l l R i g h t s R e s e r v e d .H o m e w o r k 9 # 1 P a g e 1 / 11
Homework 9 #1
Class Name : MAT2058 Statistics (10wk) –
20200627 – MAT2058 Statistics VB05
Instructor Name : Bibi
Student Name : _____________________ Instructor Note :
Question 1 of 10
The records of a casualty insurance company show that, in the past, its clients have had a mean of
auto accidents per day with a variance of . The actuaries of the company claim that the variance
of the number of accidents per day is no longer equal to . Suppose that we want to carry out a
hypothesis test to see if there is support for the actuaries’ claim. State the null hypothesis and the
alternative hypothesis that we would use for this test.
H0:
H1:
Question 2 of 10
1.9
0.0016
0.0016
H0
H1
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A laboratory claims that the mean sodium level, , of a healthy adult is mEq per liter of blood. To
test this claim, a random sample of adult patients is evaluated. The mean sodium level for the
sample is mEq per liter of blood. It is known that the population standard deviation of adult sodium
levels is mEq. Assume that the population is normally distributed. Can we conclude, at the level
of significance, that the population mean adult sodium level differs from that claimed by the laboratory?
Perform a two-tailed test. Then answer the questions below.
Carry your intermediate computations to at least three decimal places, and round your responses as
specified in the questions.
1. The null hypothesis:
H0:
2. The alternative hypothesis:
H1:
3. The type of test statistic:
a. Z
b. t
c. Chi-Square
d. F
Degrees of freedom (if applicable):
4. The value of the test statistic:
(Round to at least three decimal places.)
5. The two critical values at the level of significance:
(Round to at least three decimal places.)
6. Can we conclude that the population mean adult sodium level differs from that claimed by the
laboratory?
a. Yes b. No
Question 3 of 10
The mean SAT score in mathematics is . The founders of a nationwide SAT preparation course claim
that graduates of the course score higher, on average, than the national mean. Suppose that the
founders of the course want to carry out a hypothesis test to see if their claim has merit. State the null
hypothesis and the alternative hypothesis that they would use.
H0:
H1:
Question 4 of 10
141
19
134
11 0.01
0.01
488
H0 H1
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A leasing firm claims that the mean number of miles driven annually, , in its leased cars is less than
miles. A random sample of cars leased from this firm had a mean of annual miles driven.
It is known that the population standard deviation of the number of miles driven in cars from this firm is
miles. Assume that the population is normally distributed. Is there support for the firm’s claim at
the level of significance?
Perform a one-tailed test. Then answer the questions below.
Carry your intermediate computations to at least three decimal places, and round your responses as
specified in the questions.
1. The null hypothesis:
H0:
2. The alternative hypothesis:
H1:
3. The type of test statistic:
a. Z
b. t
c. Chi-Square
d. F
Degrees of freedom (if applicable):
4. The value of the test statistic:
(Round to at least three decimal places.)
5. The p-value:
(Round to at least three decimal places.)
6. Can we support the leasing firm’s claim that the mean number of miles driven annually is less than
13400 miles?
a. Yes b. No
Question 5 of 10
A decade-old study found that the proportion of high school seniors who felt that “getting rich” was an
important personal goal was . Suppose that we have reason to believe that this proportion has
changed, and we wish to carry out a hypothesis test to see if our belief can be supported. State the null
hypothesis and the alternative hypothesis that we would use for this test.
H0:
H1:
Question 6 of 10
13400 9 13035
2400
0.1
67%
H0 H1
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The mean SAT score in mathematics, , is . The standard deviation of these scores is . A special
preparation course claims that its graduates will score higher, on average, than the mean score . A
random sample of students completed the course, and their mean SAT score in mathematics was
. Assume that the population is normally distributed. At the level of significance, can we conclude
that the preparation course does what it claims? Assume that the standard deviation of the scores of
course graduates is also .
Perform a one-tailed test. Then answer the questions below.
Carry your intermediate computations to at least three decimal places, and round your responses as
specified in the questions.
1. The null hypothesis:
H0:
2. The alternative hypothesis:
H1:
3. The type of test statistic:
a. Z
b. t
c. Chi-Square
d. F
Degrees of freedom (if applicable):
4. The value of the test statistic:
(Round to at least three decimal places.)
5. The critical value at the level of significance:
(Round to at least three decimal places.)
6. Can we support the preparation course’s claim that its graduates score higher in SAT?
a. Yes b. No
Question 7 of 10
The records of a casualty insurance company show that, in the past, its clients have had a mean of
auto accidents per day with a variance of . The actuaries of the company claim that the variance
of the number of accidents per day is no longer equal to . Suppose that we want to carry out a
hypothesis test to see if there is support for the actuaries’ claim. State the null hypothesis and the
alternative hypothesis that we would use for this test.
H0:
H1:
Question 8 of 10
530 43
530
42 546
0.05
43
0.05
1.7
0.0016
0.0016
H0
H1
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An electronics manufacturing process has a scheduled mean completion time of minutes. It is claimed
that, under new management, the mean completion time, , is less than minutes. To test this claim,
a random sample of completion times under new management was taken.
The sample had a mean completion time of minutes and a standard deviation of minutes. Assume
that the population of completion times under new management is normally distributed. At the
level of significance, can it be concluded that the mean completion time, , under new management is
less than the scheduled mean?
Perform a one-tailed test. Then answer the questions below.
Carry your intermediate computations to at least three decimal places and round your answers as
specified in the questions.
1. The null hypothesis:
H0:
2. The alternative hypothesis:
H1:
3. The type of test statistic:
a. Z
b. t
c. Chi-Square
d. F
Degrees of freedom (if applicable):
4. The value of the test statistic:
(Round to at least three decimal places.)
5. The critical value at the level of significance:
(Round to at least three decimal places.)
6. At the level, can it be concluded that the mean completion time under new management is
less than the scheduled mean?
a. Yes b. No
Question 9 of 10
65
65
10
64 9
0.05
0.05
0.05
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It seems these days that college graduates who are employed full-time work more than -hour weeks.
Data are available that can help us decide if this is true. A survey was recently sent to a group of adults
selected at random. There were respondents who were college graduates employed full-time. The
mean number of hours worked per week by these respondents was hours, with a standard
deviation of hours.
Assume that the population of hours worked per week by college graduates employed full-time is
normally distributed with mean . Can we conclude that is greater than hours? Use the level
of significance.
Perform a one-tailed test. Then answer the questions below.
Carry your intermediate computations to at least three decimal places and round your answers as
specified in the questions.
1. The null hypothesis:
H0:
2. The alternative hypothesis:
H1:
3. The type of test statistic:
a. Z
b. t
c. Chi-Square
d. F
Degrees of freedom (if applicable):
4. The value of the test statistic:
(Round to at least three decimal places.)
5. The p-value:
(Round to at least three decimal places.)
6. Can we conclude, at the 0.05 level of significance, that the mean number of hours worked per
week by college graduates is greater than hours?
a. Yes b. No
Question 10 of 10
40
16
16 46
10
40 0.05
40
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Heights were measured for a random sample of plants grown while being treated with a particular
nutrient. The sample mean and sample standard deviation of those height measurements were
centimeters and centimeters, respectively.
Assume that the population of heights of treated plants is normally distributed with mean . Based on
the sample, can it be concluded that is different from centimeters? Use the level of significance.
Perform a two-tailed test. Then answer the questions below.
Carry your intermediate computations to at least three decimal places and round your answers as
specified in the questions.
1. The null hypothesis:
H0:
2. The alternative hypothesis:
H1:
3. The type of test statistic:
a. Z
b. t
c. Chi-Square
d. F
Degrees of freedom (if applicable):
4. The value of the test statistic:
(Round to at least three decimal places.)
5. The two critical values at the level of significance:
(Round to at least three decimal places.)
6. At the 0.1 level of significance, can it be concluded that the population mean height of treated
plants is different from centimeters?
a. Yes b. No
22
32
9
36 0.1
0.1
36
