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STA 2023 Lecture Notes - Lecture 46: Null Hypothesis, Contingency Table, Analysis Of Variance

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lavenderpig501
19 Dec 2016
School
FGCU
Department
Statistics
Course
STA 2023
Professor
Hair

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Document Summary

When data can be calculated in table form in terms of frequencies, several types of hypotheses can be tested by using the chi-square test. The test of independence of variables is used to determine whether two variables are independent of or related to each other when a single sample is selected. The test of homogeneity of proportions is used to determine whether the proportions for a variable are equal when several samples are selected from different populations. The chi-square goodness-of-fit test can be used to test the independence of two variables. The hypothesis are: ho: there is no relationship between two variables, h1: there is a relationship between two variables. If the null hypothesis is rejected, there is some relationship between the variables. In order to test the null hypothesis, one must compute the expected frequencies, assuming the null hypothesis is true. When data are arranged in table form for the independence test, the table is called a contingency table.

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Related Questions

Grade Two different professors teach an Introductory Statistics course. The table shows the distribution of final grades they reported. We wonder whether one of these professors is an "easier" grader.

  Prof A Prof B
A 3 9
B 11 12
C 14 8
D 9 2
E 3 1

a.) Will you test goodness-of-fit, homogeneity, or independence?

b.)Write appropriate null hypothesis.

c.) Find the expected counts for each cell, and explain why the chi-square procedures are not appropriate. 

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).