Question

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
mean annual premium in Pennsylvania is lower than the national mean
annual premium.

*H*
_{0}: *μ* - Select your answer -greater than
1,494greater than or equal to 1,494equal to 1,494less than or equal
to 1,494less than 1,494not equal to 1,494

*H* _{a}: *μ* - Select your answer -greater
than 1,494greater than or equal to 1,494equal to 1,494less than or
equal to 1,494less than 1,494not equal to 1,494

**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 .005between .005 and .01between
.01 and .025between .025 and .05between .05 and .10between .10 and
.20greater than .20

What is your
conclusion?

- Select your answer -The population mean automobile premium is
higher in Pennsylvania than the national mean.The population mean
automobile premium is lower in Pennsylvania than the national
mean.

Answer #1

a)

null hypothesis: HO: | μ | >= | 1494 | |

Alternate Hypothesis: Ha: | μ | < | 1494 |

b)

point estimate of difference =1439-1494 = -55

c)

standard errror of mean = |
s_{x}=s/√n= |
30.0000 | |

test statistic t = |
(x-μ)*√n/s_{x}= |
-1.833 | |

p value = | 0.0396 |

p value is between .025 and .05

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