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Chapter 8: Q77E (page 500)

Specify the appropriate rejection region for testing \({H_0}:\sigma _1^2 = \sigma _2^2\) in each of the following situations:

  1. \({H_a}:\sigma _1^2 > \sigma _2^2\,\alpha = .05,\,{n_1} = 25,{n_2} = 20\)

Short Answer

Expert verified
  1. The rejection region for right tailed test is given by \(F > 2.1141\)

Step by step solution

01

Given Information

The hypothesis are given by

\(\begin{aligned}{H_0}:\sigma _1^2 = \sigma _2^2\\{H_a}:\sigma _1^2 > \sigma _2^2\end{aligned}\)

The level of significance is 0.05

02

Compute degrees of freedom

\(\begin{aligned}{v_1} &= {n_1} - 1\\ &= 25 - 1\\ &= 24\\{v_2} &= {n_2} - 1\\ &= 20 - 1\\ &= 19\end{aligned}\)

03

Test statistic

The test statistic is computed as

\(F = \frac{{s_1^2}}{{s_2^2}}\)

04

Critical value

For,

\(\alpha = 0.05\,and\,{v_1} = 24\;and\,{v_2} = 19\)

The critical value is

\({F^ \bullet } = {F_{0.05}}\left( {24,19} \right) = 2.1141\)

05

Decision-rule

The rejection region for right tailed test is given by

\(\begin{aligned}F > {F^ \bullet }\\F > 2.1141\end{aligned}\)

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Most popular questions from this chapter

Given that xis a binomial random variable, compute P(x)for each of the following cases:

a. n= 7, x= 3, p= .5

b. n= 4, x= 3, p= .8

c. n= 15, x= 1, p= .1

Studies have established that rudeness in the workplace can lead to retaliatory and counterproductive behaviour. However, there has been little research on how rude behaviours influence a victim鈥檚 task performance. Such a study was conducted, and the results were published in the Academy of Management Journal (Oct. 2007). College students enrolled in a management course were randomly assigned to two experimental conditions: rudeness condition (students) and control group (students). Each student was asked to write down as many uses for a brick as possible in minutes. For those students in the rudeness condition, the facilitator displayed rudeness by generally berating students for being irresponsible and unprofessional (due to a late-arriving confederate). No comments were made about the late-arriving confederate to students in the control group. The number of different uses for brick was recorded for each student and is shown below. Conduct a statistical analysis (at 伪=0.01) to determine if the true mean performance level for students in the rudeness condition is lower than the actual mean performance level for students in the control group.

The data is given below

Control Group:

124516217201920191023160491317130212117311119912185213015421211101311361013161228191230


Rudeness Condition:

411181196511912757311191110789107114135478381591610071513921310

Enough money has been budgeted to collect independent random samples of size n1=n2=100from populations 1 and 2 to estimate localid="1664867109106" 渭1-渭2. Prior information indicates that 蟽1=蟽2=10. Have sufficient funds been allocated to construct a 90% confidence interval for渭1-渭2of width 5 or less? Justify your answer.

Question: Independent random samples from approximately normal populations produced the results shown below.

Sample 1

Sample 2

52 33 42 4441 50 44 5145 38 37 4044 50 43

52 43 47 5662 53 61 5056 52 53 6050 48 60 55

a. Do the data provide sufficient evidence to conclude that (渭1-渭2)>10? Test using伪=0.1.

b. Construct a confidence interval for (渭1-渭2). Interpret your result.

A paired difference experiment produced the following results:

nd=38,x炉1=92,x炉2=95.5,d炉=-3.5,sd2=21

a. Determine the values zfor which the null hypothesis 渭1鈭�渭2=0would be rejected in favor of the alternative hypothesis 渭1鈭�渭2<0 Use .role="math" localid="1652704322912" 伪=.10

b. Conduct the paired difference test described in part a. Draw the appropriate conclusions.

c. What assumptions are necessary so that the paired difference test will be valid?

d. Find a90% confidence interval for the mean difference 渭d.

e. Which of the two inferential procedures, the confidence interval of part d or the test of the hypothesis of part b, provides more information about the differences between the population means?
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