# Hypothesis Testing: P-Value and Null Value

This problem contains 4 parts based on the following information (also see attachment).

"The Florida Home Energy Commission lists the mean annual air-conditioning (A/C) expenditure for a well-insulated Central Florida home as $1.20 per square foot. Cool Crib Insulation (a home insulation company) is working hard to attract new customers. In the company's advertising, they claim that homes with their exclusive, patented insulation material have A/C costs that are below average for the region. A consumer-affairs investigator has surveyed a sample of 80 recent Cool Crib customers and listed their A/C expenditures (per square foot) in the following tab. The investigator is interested in examining whether the mean A/C expenditures for Cool Crib's clients really is less than the $1.20 per square foot average for the entire region. Based on these data, and using a significance level of 5% (i.e. = .05), provide the answers to the following questions in the spaces provided:

Report all answers to this problem to a minimum of 4 decimal places.

Using the provided sample data,(in the attached excel spreadsheet), to answer the following questions:

a. Write the expression for the correct alternative hypothesis statement for the test that must be carried out.

Ha: __________________ _________ _________

(or H1): (Population Parameter) (Operator) (Null Value)

b. Perform the hypothesis test and record the "p-value" for this test.

The p-value for this hypothesis test is: _________________ 4 decimal places

c. Which of the following statements is correct?

i) i. The mean annual A/C expenditure for Cool Crib clients appears to be significantly less than the regional average of $1.20 per square foot.

ii) ii. The mean annual A/C expenditure for Cool Crib clients appears NOT to be significantly less than the regional average of $1.20 per square foot.

Copy and past your choice from the statements above, in the space below.

d. The investigator would next (separately) like to estimate, with 99% confidence, the mean annual A/C expenditures for all Cool Crib clients. Based on the same sample data (used in parts a. thru c. above), find the range in which he can be 99% confident that the actual mean annual A/C expenditures (for all Cool Crib clients) will fall?

Upper Limit __________________

Lower Limit __________________

This entire problem in excel is attached. It has 'data and workspace' spreadsheet to do all calculations.

© BrainMass Inc. brainmass.com October 25, 2018, 9:57 am ad1c9bdddfhttps://brainmass.com/statistics/hypothesis-testing/hypothesis-testing-null-values-592654

#### Solution Preview

Please see the attachments for the solutions.

Please note that this is not ...

#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis. Formula for the calculation and Interpretations of the results are also included.

Hypothesis Testing: Null and Alternate Hypotheses, P Value

Four Hypothesis Testing problems

Problem 10.17: M&M/Mars claims that at least 20% of the M&M's in each package are the new blue color. Set up the null and alternate hypotheses to test this claim.

Problem 10.18: The computer center at a university claims that the average amount of time that students spend on-line has increased from last year's average of 1 hour per day. Set up the null and alternative hypotheses to test this claim.

Problem 10.20: Recent medical research indicates that skin cancer patients who receive a new medication for skin cancer live longer than those who do not. The average length of life prior to the development of this medication was 18 months. The medical community wishes to test the claim made by the developers of this drug. A sample of 35 patients who received the medication lived an average of 21 months. The standard deviation is 5 months.

a) Set up the null and the alternative hypotheses to test if average length of life has increased from 18 months.

b) Test your hypotheses using a = 0.05.

c) Find the p value.

d) Based on the p value, what can you conclude about the average length of life for patients who receive the vaccine?

Problem 10.22: A manufacturer of top-of-line tennis rackets claims that its Smack Em tennis racket will change a player's game. A tennis pro currently serves the ball at an average speed of 115 mph with a standard deviation of 2.5 mph. The speeds are normally distributed. The tennis pro decides to test the company's claim and records the speed of his serve for 15 balls using the Smack Em racket. The data are shown in the following table: Speed

117.3 115.9

115.1 115.2

116.0 115.0

116.2 113.0

112.9 120.8

115.4 116.9

113.8 114.4

114.2

a) Set up the null and the alternative hypotheses to test if the average service speed has increased using the new racket.

b) Test your hypotheses using a = 0.05

c) Find the p value.

d) Based on the p value, should the tennis pro invest in the new racket?