Question

A random sample of

*n*_{1} = 49

measurements from a population with population standard deviation

*σ*_{1} = 5

had a sample mean of

*x*_{1} = 8.

An independent random sample of

*n*_{2} = 64

measurements from a second population with population standard deviation

*σ*_{2} = 6

had a sample mean of

*x*_{2} = 11.

Test the claim that the population means are different. Use level of significance 0.01.(a) Check Requirements: What distribution does the sample test statistic follow? Explain.

The standard normal. We assume that both population
distributions are approximately normal with unknown standard
deviations.The Student's *t*. We assume that both population
distributions are approximately normal with unknown standard
deviations. The standard normal. We assume
that both population distributions are approximately normal with
known standard deviations.The Student's *t*. We assume that
both population distributions are approximately normal with known
standard deviations.

(b) State the hypotheses.

*H*_{0}: *μ*_{1} =
*μ*_{2}; *H*_{1}:
*μ*_{1} <
*μ*_{2}*H*_{0}:
*μ*_{1} ≠ *μ*_{2};
*H*_{1}: *μ*_{1} =
*μ*_{2} *H*_{0}:
*μ*_{1} = *μ*_{2};
*H*_{1}: *μ*_{1} >
*μ*_{2}*H*_{0}:
*μ*_{1} = *μ*_{2};
*H*_{1}: *μ*_{1} ≠
*μ*_{2}

(c) Compute

*x*_{1} − *x*_{2}.

*x*_{1} − *x*_{2} =

Compute the corresponding sample distribution value. (Test the
difference *μ*_{1} − *μ*_{2}. Round
your answer to two decimal places.)

(d) Find the *P*-value of the sample test statistic. (Round
your answer to four decimal places.)

(e) Conclude the test.

At the *α* = 0.01 level, we reject the null hypothesis
and conclude the data are not statistically significant.At the
*α* = 0.01 level, we reject the null hypothesis and conclude
the data are statistically significant. At
the *α* = 0.01 level, we fail to reject the null hypothesis
and conclude the data are not statistically significant.At the
*α* = 0.01 level, we fail to reject the null hypothesis and
conclude the data are statistically significant.

(f) Interpret the results.

Reject the null hypothesis, there is sufficient evidence that there is a difference between the population means.Fail to reject the null hypothesis, there is insufficient evidence that there is a difference between the population means. Reject the null hypothesis, there is insufficient evidence that there is a difference between the population means.Fail to reject the null hypothesis, there is sufficient evidence that there is a difference between the population means.

Answer #1

a)

The standard normal. We assume that both population distributions are approximately normal with known standard deviations

b)

H0: μ1 = μ2; H1: μ1 ≠ μ2

c)

x1 -x2 = 8 - 11 = -3

Pooled Variance

sp = sqrt(s1^2/n1 + s2^2/n2)

sp = sqrt(25/49 + 36/64)

sp = 1.0357

Test statistic,

z = (x1bar - x2bar)/sp

z = (8 - 11)/1.0357

z = -2.90

d)

P-value Approach

P-value = 0.0037

e)

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

f)

Reject the null hypothesis, there is sufficient evidence that there
is a difference between the population means

A random sample of
n1 = 49
measurements from a population with population standard
deviation
σ1 = 3
had a sample mean of
x1 = 13.
An independent random sample of
n2 = 64
measurements from a second population with population standard
deviation
σ2 = 4
had a sample mean of
x2 = 15.
Test the claim that the population means are different. Use
level of significance 0.01.
(a) Check Requirements: What distribution does the sample test
statistic follow? Explain....

A random sample of n1 = 10 regions in New
England gave the following violent crime rates (per million
population).
x1: New England Crime
Rate
3.5
3.7
4.2
4.1
3.3
4.1
1.8
4.8
2.9
3.1
Another random sample of n2 = 12 regions in
the Rocky Mountain states gave the following violent crime rates
(per million population).
x2: Rocky Mountain Crime
Rate
3.9
4.1
4.5
5.1
3.3
4.8
3.5
2.4
3.1
3.5
5.2
2.8
Assume that the crime rate distribution...

The highway department is testing two types of reflecting paint
for concrete bridge end pillars. The two kinds of paint are alike
in every respect except that one is orange and the other is yellow.
The orange paint is applied to 12 bridges, and the yellow paint is
applied to 12 bridges. After a period of 1 year, reflectometer
readings were made on all these bridge end pillars. (A higher
reading means better visibility.) For the orange paint, the mean...

The highway department is testing two types of reflecting paint
for concrete bridge end pillars. The two kinds of paint are alike
in every respect except that one is orange and the other is yellow.
The orange paint is applied to 12 bridges, and the yellow paint is
applied to 12 bridges. After a period of 1 year, reflectometer
readings were made on all these bridge end pillars. (A higher
reading means better visibility.) For the orange paint, the mean...

A comparison is made between two bus lines to determine if
arrival times of their regular buses from Denver to Durango are off
schedule by the same amount of time. For 46 randomly selected runs,
bus line A was observed to be off schedule an average time of 53
minutes, with standard deviation 15 minutes. For 60 randomly
selected runs, bus line B was observed to be off schedule an
average of 62 minutes, with standard deviation 13 minutes. Do...

The Wind Mountain archaeological site is in southwest New
Mexico. Prehistoric Native Americans called Anasazi once lived and
hunted small game in this region. A stemmed projectile point is an
arrowhead that has a notch on each side of the base. Both stemmed
and stemless projectile points were found at the Wind Mountain
site. A random sample of n1 = 60 stemmed
projectile points showed the mean length to be
x1 = 3.00 cm, with sample standard deviation
s1 =...

A random sample of n1 = 10 regions in New
England gave the following violent crime rates (per million
population).
x1: New England Crime
Rate
3.5
3.9
4.0
4.1
3.3
4.1
1.8
4.8
2.9
3.1
Another random sample of n2 = 12 regions in
the Rocky Mountain states gave the following violent crime rates
(per million population).
x2: Rocky Mountain Crime
Rate
3.9
4.3
4.7
5.3
3.3
4.8
3.5
2.4
3.1
3.5
5.2
2.8
Assume that the crime rate distribution...

In the journal Mental Retardation, an article reported
the results of a peer tutoring program to help mildly mentally
retarded children learn to read. In the experiment, the mildly
retarded children were randomly divided into two groups: the
experimental group received peer tutoring along with regular
instruction, and the control group received regular instruction
with no peer tutoring. There were n1 =
n2 = 30 children in each group. The
Gates-MacGintie Reading Test was given to both groups before
instruction...

The Wind Mountain archaeological site is in southwest New
Mexico. Prehistoric Native Americans called Anasazi once lived and
hunted small game in this region. A stemmed projectile point is an
arrowhead that has a notch on each side of the base. Both stemmed
and stemless projectile points were found at the Wind Mountain
site. A random sample of n1 = 55 stemmed projectile points showed
the mean length to be x1 = 3.00 cm, with sample standard deviation
s1 =...

REM (rapid eye movement) sleep is sleep during which most dreams
occur. Each night a person has both REM and non-REM sleep. However,
it is thought that children have more REM sleep than adults†.
Assume that REM sleep time is normally distributed for both
children and adults. A random sample of n1 = 9 children (9 years
old) showed that they had an average REM sleep time of x1 = 2.9
hours per night. From previous studies, it is known...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 6 minutes ago

asked 11 minutes ago

asked 18 minutes ago

asked 28 minutes ago

asked 39 minutes ago

asked 48 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago