Question

Question 14

Suppose that the mean price of a home in Denver, Colorado in 2008 was 225.3 thousand dollars. A random sample of 49 homes sold in 2010 had a mean price of 198.7 thousand dollars. A real estate firm wants to test to see if the mean price in 2010 differs from the from mean price in 2008. Assume that the population standard deviation is 140. Perform the hypothesis test and compute the P-value.

Write down your P-value. You will need it for the next question.

Round your answer to four decimal places (for example: 0.2305). Write only a number as your answer.

Question 15

Recall the previous question where the real estate firm wants to see if the mean price of homes in 2010 have differed from the mean price in 2008. Based on your P-value, what is the conclusion if we test at the 0.05 level of significance?

Question 15 options:

There is evidence to conclude that the mean price of homes in 2010 differ from the mean price in 2008.

This is not enough evidence to conclude that the mean price of homes in 2010 differ from the mean price in 2008.

There is evidence to conclude that the mean price of homes in 2010 do not differ from the mean price in 2008.

There is not enough evidence to conclude that the mean price of homes in 2010 do not differ from the mean price in 2008.

Question 16

A random sample of 64 second-graders in a certain school district are given a standardized mathematics skills test. The sample mean score is 51.12 . Assume the standard deviation for the population of test scores is 15. The nationwide average score on this test is 50. The school superintendent wants to know whether the second-graders in her school district have greater math skills than the nationwide average. Perform the hypothesis test and compute the P-value.

Write down your P-value. You will need it for the next question.

Round your answer to four decimal places (for example: 0.2305). Write only a number as your answer.

part 2

Recall the previous question where the school superintendent wanted to know whether second-graders in her school district have greater math skills than the nationwide average. Based on your P-value, what is the conclusion if we test at the 0.05 level of significance?

options:

There is evidence to conclude that the second-graders in her district do not have greater math skills.

There is evidence to conclude that the second-graders in her district have greater math skills.

This is not enough evidence to conclude that the second-graders in her district have greater math skills.

There is not enough evidence to conclude that the second-graders in her district do not have greater math skills.

Answer 1

14. As the population standard deviation is known, we will perform a one-sample z-test:

Ho: mu = 225.3
Ha: mu =/ 225.3

n = 49
x = 198.7
mu = 225.3
σ = 140

z = (198.7 - 225.3)/(140/√49) = -1.33
p-value associated with the z-value is 0.1835

15. As the p-value = 0.1835 > 0.05, we fail to reject the null hypothesis.

Our conclusion is: There is not enough evidence to conclude that the mean price of homes in 2010 differ from the mean price in 2008.
Option B) is correct

16. Ho: mu = 50
Ha: mu > 50

This is a one-tailed test.

x = 51.12
mu = 50
σ = 15
n = 64

z = (51.12 - 50)/(15/8) = 0.597

16. From the z-table, p-value = 0.2753

We fail to reject the null hypothesis.

We conclude that This is not enough evidence to conclude that the second-graders in her district have greater math skills. Option C) is correct