The Insure.com website reports that the mean annual premium for automobile insurance in the United States was $1,503 in March 2014. Being from Pennsylvania at that time, you believed automobile insurance was cheaper there and decided 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 $1,425 with a standard deviation of s = $160. (a) Develop a hypothesis test that can be used to determine whether the mean annual premium in Pennsylvania is lower than the national mean annual premium. H0: μ < 1,503 Ha: μ ≥ 1,503 H0: μ ≥ 1,503 Ha: μ < 1,503 H0: μ > 1,503 Ha: μ ≤ 1,503 H0: μ = 1,503 Ha: μ ≠ 1,503 H0: μ ≤ 1,503 Ha: μ > 1,503 (b) What is a point estimate in dollars of the difference between the mean annual premium in Pennsylvania and the national mean? (Use the mean annual premium in Pennsylvania minus the national mean.) ($ ) (c) At ? = 0.05, test for a significant difference. Find the value of the test statistic. (Round your answer to three decimal places.) ( ) Find the p-value. (Round your answer to four decimal places.) p-value = ( ) State your conclusion. Reject H0. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean. Do not reject H0. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean. Do not reject H0. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean. Reject H0. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.

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Description: The Insure.com website reports that the mean annual premium for automobile insurance in the United States was $1,503 in March 2014. Being from Pennsylvania at that time, you believed automobile insurance was cheaper there and decided to develop stati

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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The Insure.com website reports that the mean annual premium for automobile insurance in the United States was $1,503 in March 2014. Being from Pennsylvania at that time, you believed automobile insurance was cheaper there and decided 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 $1,425 with a standard deviation of s = $160.

(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.

H₀: μ < 1,503

H_a: μ ≥ 1,503

H₀: μ ≥ 1,503

H_a: μ < 1,503

H₀: μ > 1,503

H_a: μ ≤ 1,503

H₀: μ = 1,503

H_a: μ ≠ 1,503

H₀: μ ≤ 1,503

H_a: μ > 1,503

(b)

What is a point estimate in dollars of the difference between the mean annual premium in Pennsylvania and the national mean? (Use the mean annual premium in Pennsylvania minus the national mean.)

($ )

test for a significant difference.

Find the value of the test statistic. (Round your answer to three decimal places.)

( )

Find the p-value. (Round your answer to four decimal places.)

p-value = ( )

State your conclusion.

Reject H₀. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.

Do not reject H₀. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.

Do not reject H₀. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.

Reject H₀. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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