According to the National Association of Realtors, it took an average of three weeks to sell a home in 2017. Suppose data for the sale of 39 randomly selected homes sold in Greene County, Ohio, in 2017 showed a sample mean of 3.6 weeks with a sample standard deviation of 2 weeks. Conduct a hypothesis test to determine whether the number of weeks until a house sold in Greene County differed from the national average in 2017. Use α = 0.05 for the level of significance, and state your conclusion. (a) State the null and alternative hypothesis. (Enter != for ≠ as needed.) H0: Ha: (b) 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 = (c) State your conclusion. (A)Reject H0. There is not a statistically significant difference between the national average time to sell a home and the mean time to sell a home in Greene County. (B)Do not reject H0. There is a statistically significant difference between the national average time to sell a home and the mean time to sell a home in Greene County. (C) Reject H0. There is a statistically significant difference between the national average time to sell a home and the mean time to sell a home in Greene County. (D)Do not reject H0. There is not a statistically significant difference between the national average time to sell a home and the mean time to sell a home in Greene County.

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Description: According to the National Association of Realtors, it took an average of three weeks to sell a home in 2017. Suppose data for the sale of 39 randomly selected homes sold in Greene County, Ohio, in 2017 showed a sample mean of 3.6 weeks with a sample

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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According to the National Association of Realtors, it took an average of three weeks to sell a home in 2017. Suppose data for the sale of 39 randomly selected homes sold in Greene County, Ohio, in 2017 showed a sample mean of 3.6 weeks with a sample standard deviation of 2 weeks. Conduct a hypothesis test to determine whether the number of weeks until a house sold in Greene County differed from the national average in 2017. Use

α = 0.05 for the level of significance, and state your conclusion.

(a) State the null and alternative hypothesis. (Enter != for ≠ as needed.)

H₀:

H_a:

(b) 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 =

(A)Reject H₀. There is not a statistically significant difference between the national average time to sell a home and the mean time to sell a home in Greene County.

(B)Do not reject H₀. There is a statistically significant difference between the national average time to sell a home and the mean time to sell a home in Greene County.

(C) Reject H₀. There is a statistically significant difference between the national average time to sell a home and the mean time to sell a home in Greene County.

(D)Do not reject H₀. There is not a statistically significant difference between the national average time to sell a home and the mean time to sell a home in Greene County.

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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