Chapter 8: Q85E (page 452)
Question: Find the following probabilities for the standard normal random variable z:
Short Answer
Answer
A random variable is a mathematical expression of a statistical study's result.
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Chapter 8: Q85E (page 452)
Question: Find the following probabilities for the standard normal random variable z:
Answer
A random variable is a mathematical expression of a statistical study's result.
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Independent random samples from normal populations produced the results shown in the next table.
Sample 1 | Sample 2 |
a. Calculate the pooled estimate of .
b. Do the data provide sufficient evidence to indicate that ? Test using .
c. Find a confidence interval for .
d. Which of the two inferential procedures, the test of hypothesis in part b or the confidence interval in part c, provides more information about ?
Given the following values of , , and , form a 90% confidence interval for
a.
b.
c.
d.
Drug content assessment. Refer to Exercise 8.16 (p. 467)and the Analytical Chemistry (Dec. 15, 2009) study in which scientists used high-performance liquid chromatography to determine the amount of drug in a tablet. Recall that 25 tablets were produced at each of two different, independent sites. The researchers want to determine if the two sites produced drug concentrations with different variances. A Minitab printout of the analysis follows. Locate the test statistic and p-value on the printout. Use these values and to conduct the appropriate test for the researchers.

Test and CI for two Variances: Content vs Site
Method
Null hypothesis
Alternative hypothesis
F method was used. This method is accurate for normal data only.
Statistics
Site N St Dev Variance 95% CI for St Devs
1 25 3.067 9.406 (2.195,4.267)
2 25 3.339 11.147 (2.607,4.645)
Ratio of standard deviation =0.191
Ratio of variances=0.844
95% Confidence Intervals
Method CI for St Dev Ratio CI Variance Ratio
F (0.610, 1.384) (0.372, 1.915)
Tests
Method DF1 DF2 Test statistic p-value
F 24 24 0.84 0.681

A random sample of n observations is selected from a normal population to test the null hypothesis that . Specify the rejection region for each of the following combinations of and .
a.
b.
c.
d.
e.
f.
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’s 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 ) 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: |
Rudeness Condition: |
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