Question

A researcher is interested in seeing if the average income of
rural families is different than that of urban families. To see if
his claim is correct he randomly selects 42 families from a rural
area and finds that they have an average income of $68532 with a
population standard deviation of $832. He then selects 47 families
from a urban area and finds that they have an average income of
$67140 with a population standard deviation of $809. Perform a
hypothesis test using a significance level of 0.10 to test his
claim. Let rural families be sample 1 and urban familis be sample
2.

The correct hypotheses are:

- H0:μ1≤μ2H0:μ1≤μ2

HA:μ1>μ2HA:μ1>μ2 (claim) - H0:μ1≥μ2H0:μ1≥μ2

HA:μ1<μ2HA:μ1<μ2 (claim) - H0:μ1=μ2H0:μ1=μ2

HA:μ1≠μ2HA:μ1≠μ2 (claim)

Since the level of significance is 0.10 the critical value is
1.645 and -1.645

The test statistic is: (round to 3 places)

The p-value is: (round to 3 places)

The decision can be made to:

- reject H0H0
- do not reject H0H0

The final conclusion is that:

- There is enough evidence to reject the claim that the average income of rural families is different than that of urban families.
- There is not enough evidence to reject the claim that the average income of rural families is different than that of urban families.
- There is enough evidence to support the claim that the average income of rural families is different than that of urban families.
- There is not enough evidence to support the claim that the average income of rural families is different than that of urban families.

Answer #1

Null Hypothesis, H0: μ1 = μ2

Alternative Hypothesis, Ha: μ1 ≠ μ2

Pooled Variance

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

sp = sqrt(692224/42 + 654481/47)

sp = 174.375

Test statistic,

z = (x1bar - x2bar)/sp

z = (68532 - 67140)/174.375

z = 7.983

P-value Approach

P-value = 0.000

As P-value >= 0.1, fail to reject null hypothesis.

do not reject H0

There is not enough evidence to support the claim that the average income of rural families is different than that of urban families

A random sample of 17 chemists from Washington state shows an
average salary of $43209 with a standard deviation of $832. A
random sample of 15 chemists from Florida state shows an average
salary of $49207 with a standard deviation of $809. A chemist that
has worked in both states believes that chemists in Washington make
a different amount than chemists in Florida. At αα =0.10 is this
chemist correct? Let Washington be sample 1 and Florida be sample
2....

A random sample of 24 chemists from Washington state shows an
average salary of $43261 with a standard deviation of $972. A
random sample of 24 chemists from Florida state shows an average
salary of $42312 with a standard deviation of $952. A chemist that
has worked in both states believes that chemists in Washington make
a different amount than chemists in Florida. At αα =0.05 is this
chemist correct? Let Washington be sample 1 and Florida be sample
2....

A random sample of 23 chemists from Washington state shows an
average salary of $41151 with a standard deviation of $775. A
random sample of 17 chemists from Florida state shows an average
salary of $46349 with a standard deviation of $924. A chemist that
has worked in both states believes that chemists in Washington make
a different amount than chemists in Florida. At αα=0.01 is this
chemist correct? Let Washington be sample 1 and Florida be sample
2.
The...

A recent publication states that the average closing cost for
purchasing a new home is $8927. A real estate agent believes that
the average closing cost is more than $8927. She selects 40 new
home purchases and finds that the average closing costs are $8352.
The population standard deviation of $153. Help her decide if she
is correct by testing her claim at αα=0.10.
The correct hypotheses would be:
H0:μ≤$8927H0:μ≤$8927
HA:μ>$8927HA:μ>$8927 (claim)
H0:μ≥$8927H0:μ≥$8927
HA:μ<$8927HA:μ<$8927 (claim)
H0:μ=$8927H0:μ=$8927
HA:μ≠$8927HA:μ≠$8927 (claim)
Since the...

A recent publication states that the average closing cost for
purchasing a new home is $8304. A real estate agent believes the
average closing cost is more than $8304. She selects 10 new home
purchases and finds that the average closing costs are $7150 with a
standard deviation of $420. Help her decide if she is correct by
testing her claim at αα=0.10.
The correct hypotheses would be:
H0:μ≤$8304H0:μ≤$8304
HA:μ>$8304HA:μ>$8304 (claim)
H0:μ≥$8304H0:μ≥$8304
HA:μ<$8304HA:μ<$8304 (claim)
H0:μ=$8304H0:μ=$8304
HA:μ≠$8304HA:μ≠$8304 (claim)
Since the level...

A recent publication states that the average closing cost for
purchasing a new home is $8500. A real estate agent believes that
the average closing cost is more than $8500. She selects 31 new
home purchases and finds that the average closing costs are $8029.
The population standard deviation of $361. Help her decide if she
is correct by testing her claim at αα=0.10.
The correct hypotheses would be:
H0:μ≤$8500H0:μ≤$8500
HA:μ>$8500HA:μ>$8500 (claim)
H0:μ≥$8500H0:μ≥$8500
HA:μ<$8500HA:μ<$8500 (claim)
H0:μ=$8500H0:μ=$8500
HA:μ≠$8500HA:μ≠$8500 (claim)
Since the...

A recent publication states that the average closing cost for
purchasing a new home is $8100. A real estate agent believes the
average closing cost is less than $8100. She selects 22 new home
purchases and finds that the average closing costs are $7739 with a
standard deviation of $412. Help her decide if she is correct by
testing her claim at αα=0.10.
The correct hypotheses would be:
H0:μ≤$8100H0:μ≤$8100
HA:μ>$8100HA:μ>$8100 (claim)
H0:μ≥$8100H0:μ≥$8100
HA:μ<$8100HA:μ<$8100 (claim)
H0:μ=$8100H0:μ=$8100
HA:μ≠$8100HA:μ≠$8100 (claim)
Since the level...

A manufacturer claims that the mean lifetime of its lithium
batteries is less than 1520 hours. A homeowner selects 27 of these
batteries and finds the mean lifetime to be 1498 hours with a
standard deviation of 76 hours. Test the manufacturer's claim. Use
α = 0.10.
A. P-value = 0.112 > 0.02; do not reject H0; There is not
enough evidence support the claim, that mean is less than 1500.
B. P-value = 0.072 > 0.05; do not reject...

A manufacturer claims that the mean lifetime of its lithium
batteries is less than 1500 hours. A homeowner selects 25 of these
batteries and finds the mean lifetime to be 1480 hours with a
standard deviation of 80 hours. Test the manufacturer's claim.
Use α = 0.10.
A.
P-value = 0.112 > 0.10; do not reject H0; There is not enough
evidence support the claim, that mean is less than 1500.
B.
P-value = 0.112 > 0.05; do not reject...

The average income of 10 families who reside in a large
metropolitan East coast city is $62,456. The standard deviation is
$9652. The average income of 12 families who reside in a rural area
of the Midwest is $60,213, with a standard deviation of $2009. What
are the results if you want to determine at α = 0.05 if there is a
difference in the income between families who live in the cities
and those who live in the rural...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 22 minutes ago

asked 25 minutes ago

asked 33 minutes ago

asked 49 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago