Question

The mean annual premium for automobile insurance in the United
States is $1,501. Being from Pennsylvania, you believe automobile
insurance is cheaper there and wish to develop statistical support
for your opinion. A sample of 25 automobile insurance policies from
the state of Pennsylvania showed a mean annual premium of $1,442
with a standard deviation of *s*= $155.

If required, enter negative values as negative numbers.

**a.** Develop a hypothesis test that can be used
to determine whether the mean annual premium in Pennsylvania is
lower than the national mean annual premium.

*H* 0: *μ* - Select your answer: (greater than
1,501), (greater than or equal to 1,501), (equal to 1,501), (less
than or equal to 1,501), (less than 1,501), (not equal to
1,501)

*H* a: *μ* - Select your answer: (greater than
1,501), (greater than or equal to 1,501), (equal to 1,501), (less
than or equal to 1,501), (less than 1,501), (not equal to
1,501)

**b.** What is a point estimate of the difference
between the mean annual premium in Pennsylvania and the national
mean (to the nearest dollar)?

$ (___)

**c.** At *α* = .05, test for a significant
difference by completing the following.

Calculate the value of the test statistic (to 2 decimals).(___)

The *p*-value is - Select your answer: (less than .005),
(between .005 and .01), (between .01 and .025), (between .025 and
.05), (between .05 and .10),(between .10 and .20), (greater than
.20).

What is your conclusion?

- Select your answer -

1. The population mean automobile premium is higher in Pennsylvania than the national mean)

2. The population mean automobile premium is lower in Pennsylvania than the national mean.Item 6

Answer #1

The statistical software output for this problem is:

**One sample T summary hypothesis test:**

μ : Mean of population

H_{0} : μ = 1501

H_{A} : μ < 1501

**Hypothesis test results:**

Mean |
Sample Mean |
Std. Err. |
DF |
T-Stat |
P-value |
---|---|---|---|---|---|

μ | 1442 | 31 | 24 | -1.9032258 | 0.0345 |

Hence,

a) Ho: μ greater than or equal to 1,501

Ha: μ less than 1501

b) Point estimate of difference = 1442 - 1501 = -59

c) Test statistic = -1.90

p - Value is between 0.025 and 0.05

The population mean automobile premium is lower in Pennsylvania than the national mean.

The mean annual
premium for automobile insurance in the United States is $1,494.
Being from Pennsylvania, you believe automobile insurance is
cheaper there and wish to develop statistical support for your
opinion. A sample of 25 automobile insurance policies from the
state of Pennsylvania showed a mean annual premium of $1,439 with a
standard deviation of s = $150.
If required, enter
negative values as negative numbers.
a.
Develop a hypothesis test that can be used to determine whether the...

The mean annual premium for automobile insurance in the United
States is $1,491. Being from Pennsylvania, you believe automobile
insurance is cheaper there and wish to develop statistical support
for your opinion. A sample of 25 automobile insurance policies from
the state of Pennsylvania showed a mean annual premium of $1,432
with a standard deviation of s = $150. If required, enter negative
values as negative numbers.
a. Develop a hypothesis test that can be used to determine
whether the...

The ABC insurance INC. reports that the mean annual premium for
automobile insurance in the United States was $1608 in summer 2018.
However, you believed automobile insurance was cheaper in North
Carolina and decided to develop statistical support for your
opinion. A sample of 25 automobile insurance policies from the
state of North Carolina showed a mean annual premium of $1560 with
a standard deviation of s = $165.
a. Develop a hypothesis test that can be used to determine...

The average annual premium for automobile insurance in the
United States is $1526. A representative sample of annual premiums
for the state of Michigan is contained in the Excel Online file
below. Assume the population is approximately normal. Construct a
spreadsheet to answer the following questions.
Annual Premium
Formula Used
1936
Sample Size
#N/A
3108
2379
Point Estimate of Mean (to the whole)
#N/A
2766
2560
Standard Deviation (4 decimals)
#N/A
2902
2621
Confidence Coefficient
0.95
2598
2640
Level of...

A shareholders' group, in lodging a protest, claimed that the
mean tenure for a chief executive office (CEO) was at least ten
years. A survey of companies reported in the Wall Street Journal
found a sample mean tenure of x̄ = 8.66 years for
CEOs with a standard deviation of s = 7.39 years.
a. Formulate hypotheses that can be used to
challenge the validity of the claim made by the shareholders'
group.
H0 : μ __________ 10 (less than,...

The following data on price ($) and the overall score for 6
stereo headphones that were tested by Consumer Reports were as
follows.
Brand
Price
Score
Bose
190
78
Scullcandy
150
76
Koss
85
67
Phillips/O'Neill
80
57
Denon
80
40
JVC
45
27
a. Does the t test indicate a significant
relationship between price and the overall score?
The test t-Conclusion at α = .05
t = (to 2 decimal places.)
p-value is - Select your answer -less than .02,...

2. “In attempting to determine the population mean annual
automobile insurance premium, you draw a sample of 25 automobile
insurance policies. This sample has a sample mean annual premium of
$1440 and a sample standard deviation of s=$165.
a. Construct a 99% confidence interval for the population mean
annual automobile insurance premium.
b. Assuming everything else is fixed, what happens to the margin
of error as the sample size increases.

The calculations for a factorial experiment involving four
levels of factor A, three levels of factor B, and three
replications resulted in the following data: SST=286, SSA=24,
SSB=22, SSAB=185..
Set up the ANOVA table and test for significance using a=.05.
Show entries to 2 decimals, if necessary. If the answer is zero
enter “0”.
Source of Variation
Sum of Squares
Degrees of Freedom
Mean Square
F
p-value
Factor A
Factor B
Interaction
Error
Total
The -value for Factor A is...

A factorial experiment was designed to test for any significant
differences in the time needed to perform English to foreign
language translations with two computerized language translators.
Because the type of language translated was also considered a
significant factor, translations were made with both systems for
three different languages: Spanish, French, and German. Use the
following data for translation time in hours.
Language
Spanish
French
German
System 1
9
12
10
13
16
14
System
2
5
18
15
9...

Test the following hypotheses by using the χ 2
goodness of fit test.
H 0:
p A = 0.2, p B = 0.4,
and p C = 0.4
Ha:
The population proportions are not
p A = 0.2 , p B = 0.4 ,
and p C = 0.4
A sample of size 200 yielded 40 in category A, 120 in category
B, and 40 in category C. Use = .01 and test to see
whether the proportions are as stated...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 26 minutes ago

asked 50 minutes ago

asked 51 minutes ago

asked 54 minutes ago

asked 1 hour ago

asked 1 hour 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