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# Regression analysis and hypothes testing

NBC TV news, in a segment of the price of gasoline, reported last evening that the mean price nationwide is \$1.50 per gallon for self-serve regular unleaded. A random sample of 35 stations in the Milwaukee, WI area revealed that the mean price was \$1.52 per gallon and that the standard deviation was \$0.05 per gallon. At the .05 significance level, can we conclude that the price of gasoline is higher in the Milwaukee are? Calculate the p-value and interpret.

Problem 3
Babsie is a public affairs specialist at Park University. A press release issue by Babsie based on some research claims that Park University students study at least as much as the national average for students at four year universities. Across the nation, 73 percent of all students at four year universities study at least four hours per week. Seventy percent of one hundred randomly selected Park University students surveyed claimed to study more than four hours per week. Should the university retract its previous statement? Explain why or why not. (Answer using a 95 percent confidence interval.)
From Textbook P. 426 # 35. 6th Edition Basic Statistics for Business & Economics Lind. Marchal and Wathen. McGraw- Hill.

A regional commuter airline selected a random sample of 25 flights and found that the correleation between the number of passengers and the total weight, in ponds, of luggage stored in the luggage compartment is 0.94. Using the .05 significance level, can we conclude that there is a positive association between the two variables?
S. No. Movie Budget (\$ million) Box Office (\$ million) Year
1 Star Wars 11 1153 1977
2 E.T. 54 915 1962
3 Titanic 200 839 1997
4 The Empire Strikes Back 18 624 1980
5 Return of the Jadi 33 599 1983
6 Jurassic Park 63 546 1993
7 Star Wars Episode 1 110 544 1990
8 Forrest Group 55 500 1994
9 The Long King 97 474 1994
10 Shrek 2 75 415 2004
11 Spider Man 139 446 2002
12 Independence Day 75 444 1996
13 Horse Alone 101 427 1990
14 Pirates of the Caribbean: Dead Man's Chest 225 423 2006
15 LOTR: The Retern of the King 94 401 2003
16 Spider Man 2 200 385 2004
17 The Person of the Christ 25 382 2004
18 Star Wars: Episode 2 115 380 2005
19 The Lord of the Rings: The Two Towers 94 376 2002
20 The South scene 40 370 1999
21 Finding Memo 94 361 2003
22 Harry Porter and the Sorceress Store 130 360 2001
23 The Lord of the Ring: The Fellowship of the Ring 109 355 1997
24 Man in Black 90 349 2002
25 Star Wars Episode 1- Attack of the Clones 120 343 1992
27 Ghost 22 326 2003
28 Pirates of the Caribbean 125 325 1997
29 The Loss World 78 320 1991
30 Terminator 2- Judgment Day 100 328 2000
31 The Metric Reloaded 127 299 2006
32 The Chronicles of Narnia 180 292 2005
33 Harry Porter and the Goblet of fire 140 290 2001
34 Monstern's inc. 115 290 2002
35 Harry Porter and the Chamber of Secrets 100 290 2004
36 Meet the Factors 80 288 1998
37 Armageddon 140 276 2004
38 The Incredible 92 270 2004
39 Harry Porter and the Prisoner of Azkabon 130 257 2000
40 Mission Impossible 2 125 256 2006
41 Night at the Museum 120 246 2005
42 War of the World 128 234 2005
43 King Kong 207 218 2005
44 The da Vincicode 125 218 2005
45 Ice Age: The Meltdown 80 195 2005
Medagascar 124 193 2005
The Day After Tomorrow 125 193 2004
Casino Royale 150 167 2006
Troy 155 138 2004

Find the correlation between the world box office budget and world box office sales. Comment on the association between the two variables. Can we conclude that there is a significant negative correlation between movies with large budgets and large box office revenues?
53. The following data shows the retail price for 12 randomly selected laptop computers along with their corresponding processor speeds in gigahertz.
Computer Speed Price Computer Speed Price
1 2.0 \$2659 7 2.0 2929
2 1.6 1229 8 1.6 1849
3 1.6 1419 9 2.0 2819
4 1.0 1589 10 1.6 2669
5 2.0 1849 11 1.0 1249
6 1.2 1349 12 1.4 1159

a. Develop a linear equation that can be used to describe how the price depends on the processor speed. E
b. Based on your regression equation, is there one machine that seems particularly over or under priced?
c. Compute the correlation coefficient between the two variables. At the .05 significance level conduct a test of hypothesis to determine if the population correlation could be greater than zero.

Pg. 353 #34
A number of automobile accidents occur at various high-risk intersections in Teton country despite traffic lights. The traffic department claims that the modification in the type of light will reduce these accidents. The country commissioners have agreed to the proposed increment. Eight intersections were chosen at random and the lights at those intersections were modified. The numbers of minor accidents during six month period, before and after the modifications were-
Number of Accidents
A B C D E F G H
Before modification 5 7 6 4 8 9 8 10
After modification 3 7 7 0 4 6 8 2
As the 0.1 significance level is it reasonable to conclude that the modification reduces the number of accidents?
Laster Holla is the vice president for human resource for a large manufacturing company. In recent years, he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve situation, he began a fitness program in which employees exercise during their lunch hour.
Pg. #355 #40
At the 0.05 significance level, can we conclude the contaminations in measurements are lower after the use of new soap?
40. the following data on annual rates of return were collected from live stocks listed on the New York Stock Exchange (the big board) and live stock listed on NASDAQ. Assume the population standard deviation are the same. At the 10, significance level, can we conclude that the annual rates of rectum are higher on big board?
NYSE NASDAQ
17.16 15.80
17.06 15.28
15.51 10.21
8.43 17.97
25.15 7.77

#### Solution Summary

The solution provides step by step method for the calculation of regression model and test statistics . Formula for the calculation and Interpretations of the results are also included.

\$2.19