Statistics
1. The mean diastolic blood pressure for a random sample of
100 people was 98millimeters of mercury. If the standard deviation of individual blood pressure readings is known to be 10millimeters of mercury, find a 95%confidence interval for the true mean diastolic blood pressure of all people. Then complete the table below.
Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.
A. What is the lower limit of the 95% confidence?
B. What is the upper limit of the 95% confidence ?
2. Use the calculator provided to solve the following problems.
Consider a t distribution with 9 degrees of freedom. Compute P<−1.93<t1.93 Round your answer to at least three decimal places.
Consider a t distribution with 12 degrees of freedom. Find the value of c such that =P≤tc0.01 Round your answer to at least three decimal places.
3. A coin-operated drink machine was designed to discharge a mean of
7 ounces of coffee per cup. Suppose that we want to carry out a hypothesis test to see if the true mean discharge differs from 7 State the null hypothesis H0and the alternative hypothesisH1that we would use for this test.
H0=
H1=
4. A manufacturer claims that the mean lifetime, μ of its light bulbs is 51
months. The standard deviation of these lifetimes is 6 months. Sixty bulbs are selected at random, and their mean lifetime is found to be 49 months. Can we conclude, at the 0.05 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 51months?
Perform a two-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. (If necessary, consult a list of formulas .)
|
The null hypothesis |
H0= |
|
The alternative hypothesis: |
H1= |
|
The type of test statistic: |
Choose One: Z,t,Chi square, or F |
|
The value of test statistic (round to at least decimal places) |
= |
|
The two critical values At the 0.05 level of significance.(Round to at least 3 decimal places) |
= and = |
|
Can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 51 months? |
Yes or NO |
5. In a recent study, 100males used a new weight-loss supplement, and 75 of them experienced weight loss after two weeks. In the same study, 50 females used the same supplement, and 31of them experienced weight loss after two weeks. Fill in the blanks of the statement below to make the statement the most reasonable possible.
The new weight-loss supplement was less effective on in the study because
%
of them failed to lose weight after two weeks, whereas only
%
of the failed to lose weight after two weeks.
?
?
1.
The mean diastolic blood pressure for a random sample of
100
people was
98
millimeters of mercury.
If the standard deviation of individual blood
pressure readings is known to be
10
millimeters of mercury, find a
95%
confidence
interval for the true mean diastolic blood pressure of all people. Then complete the
table below.
Carry your intermediate computations to at least three decimal places. Round your
answers to one decimal place.
A.
What is the l
ower l
imit of the 95% confidence
?
B.
What is the
upper
l
imit of the 95% confidence
?
2.
Use the calculator provided to solve the following problems.
Consider a
t
distribution with
9
degrees of freedom. Compute
P
<
-
1.93
<
t
1.93
Round
your answer to at least three decimal places.
Consider a
t
distribution with
12
degrees of freedom. Find
the value of
c
such that
=
P
=
tc
0.01
Round your answer to at least three decimal places.
3.
A coin
-
operated drink machine was designed to discharge a mean of
7
ounces of coffee per cup. Suppose that we want to carry out
a hypothesis test to see
if the true mean discharge differs from
7
State the null hypothesis
H
0
and the
alternative
hypothesis
H
1
that we would use for this test.
H0=
H1=
4.
A manufacturer claims that the mean lifetime,
μ
of its light bulbs is
51
months. T
he standard deviation of these lifetimes is
6
months. Sixty bulbs are selected
at random, and their mean lifetime is found to be
49
months. Can we conclude, at the
0.05
level of significance, that the mean
lifetime of light bulbs made by this
manufacturer differs from
51
months?
Perform a two
-
tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places, and round your
responses as specified in the table.
(If necessary, consult a
list of formulas
.)
1. The mean diastolic blood pressure for a random sample of
100
people was
98
millimeters of mercury. If the standard deviation of individual blood
pressure readings is known to be
10
millimeters of mercury, find a
95%
confidence
interval for the true mean diastolic blood pressure of all people. Then complete the
table below.
Carry your intermediate computations to at least three decimal places. Round your
answers to one decimal place.
A. What is the lower limit of the 95% confidence?
B. What is the upper limit of the 95% confidence ?
2. Use the calculator provided to solve the following problems.
Consider a t distribution with
9
degrees of freedom. Compute
P<-1.93<t1.93
Round
your answer to at least three decimal places.
Consider a t distribution with
12
degrees of freedom. Find the value of
c
such that
=P=tc0.01
Round your answer to at least three decimal places.
3.
A coin-operated drink machine was designed to discharge a mean of
7
ounces of coffee per cup. Suppose that we want to carry out a hypothesis test to see
if the true mean discharge differs from
7
State the null hypothesis
H0
and the
alternative hypothesis
H1
that we would use for this test.
H0=
H1=
4.
A manufacturer claims that the mean lifetime,
μ
of its light bulbs is
51
months. The standard deviation of these lifetimes is
6
months. Sixty bulbs are selected
at random, and their mean lifetime is found to be
49
months. Can we conclude, at the
0.05
level of significance, that the mean lifetime of light bulbs made by this
manufacturer differs from
51
months?
Perform a two-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places, and round your
responses as specified in the table. (If necessary, consult a list of formulas.)