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STAT 2000 Study Guide - Final Guide: Simple Linear Regression, Decision Rule, Statistical Hypothesis Testing

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School
University of Manitoba
Department
Statistics
Course
STAT 2000
Professor
Zenaida Mateo

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Document Summary

Each year, the federal trade commission tests the tar and nicotine content of various brands of cigarettes in the united. Data for a sample of eight brands is collected, and we would like to conduct a hypothesis test at the 5% level of significance to determine whether the tar content of cigarettes can be predicted by their nicotine content. The data are analyzed using an analysis of variance, and the anova table (with some values missing) is shown below: The p-value of the appropriate test of significance is between and (e) if we used the critical value method to conduct the test, the decision rule would be to reject h0 if vs. ha: (a) 69. 90 (b) the estimate of the parameter is vs. ha : (c) this is the coefficient of determination (d) h0 : Test statistic is f = 32. 62, we look under table e with 1 and 6 degrees of freedom and we see.

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Related Questions

Hypothesis testing with ANOVA opinions about whether caffeine enhances test performance differ. You design a study to test the impact of drinks with different caffeine contents on students' test-taking abilities. You choose 21 students at random from your introductory psychology course to participate in your study. You randomly assign each student to one of three drinks, each with a different caffeine concentration, such that there are seven students assigned to each drink. You then give each of them a plain capsule containing the precise quantity of caffeine that would be consumed in their designated drink and have them take an arithmetic test 15 minutes later.

The students receive the following arithmetic test scores:

  Cola Black Tea Coffee  
Caffeine Content (mg/oz) 2.9 5.9 13.4  
  85 85 92 ∑X2 = 147,641
  86 89 87 G = 1,755
  82 82 80 N = 21
  75 75 89 k = 3
  66 88 96  
  78 76 83  
  87 82 92  
  T1 = 559 T2 = 559 T3 = 559  
  SS1 = 338.86 SS2 = 338.86 SS3 = 338.86  
  n1 = 7 n2 = 7 n3 = 7  
  M1 = 79.8571 M2 = 79.8571 M3 = 79.8571  

1.) You plan to use an ANOVA to test the impact of drinks with different caffeine contents on students' test-taking abilities. What is the null hypothesis?

(a) The population mean test score for the cola population is different from the population mean test score for the black tea population.

(b) The population mean test scores for all three treatments are equal.

(c) The population mean test scores for all three treatments are different.

(d) The population mean test scores for all three treatments are not all equal.

 

2.) Calculate the degrees of freedom and the variances for the following ANOVA table:

Source SS df MS
Between - - -
Within 702.28 - -
Total 973.14 -  

 

The formula for the F-ratio is:

 

 

3.) Using words, the formula of the F-ratio can be written as:

 

 

4.) Using the data from the ANOVA table given, the F-ratio can be written as:

 

5.) Calculate for F-ratio:

 

 

6.) At the level of significance, what is your conclusion?

(a)You can reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance.

(b)You cannot reject the null hypothesis; caffeine does appear to affect test performance.

(c)You cannot reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance.

(d)You can reject the null hypothesis; caffeine does appear to affect test performance.

Problem 1 (2 points). Every month a clothing store conducts an inventory and calculates the losses due to theft. The store would like to reduce these losses and is considering two methods to do so: the first is to hire a security guard and the second is to install cameras. The manager of the store has conducted the experiment: During the first 6 months he hired a security guard (method 1) and during the next 6 months he installed cameras (method 2). The monthly losses were reported as follows:

Security guard 350 289 407 398 470 259 Cameras 488 301 276 380 421 425

a/ Test with a=0.05 to determine whether there is enough evidence to conclude that expected monthly loss when installing cameras differs from 382. b/Since the cameras are cheaper than the guard, the manager would prefer to install the cameras unless there was enough evidence to infer that the guard was better. Conduct a hypothesis testing to advise what the manager should do? (Assuming equal variances and using a= 0.05)

Problem 2 (2 points). A supermarket chain performed a survey to help determine desirable locations for its new stores. The management of the chain wanted to know whether a linear relationship exists between weekly take home pay (s) and weekly food expenditures (y). A random sample of eight households produced the data shown in the following table Household 1 3 7 8 2 4 5 6 550 450 560 340 510 710 470 660

170 100 160 80 120 190 140 140 Y

a/ Find the least square regression line.

b/Perform the test Ho: Bi=0, H4: B10 (using a = 0.05) to determine whether there is enough evidence to infer that a linear relationship exists between weekly take home pay (s) and weekly food expenditures (y).