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# Hypothesis Testing of Mean & Variance

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The Computer Anxiety Rating Scale (CARS) measures an individual's level of computer anxiety, on a scale from 20 ( no anxiety) to 100 (highest level of anxiety). Researchers at Miami University administered CARS to 172 business students. One of the objectives of the study was to determine whether there is a difference between the level of computer anxiety experienced by female students and male students. They found the following:

Males Females
(sample mean) X: 40.26 36.85
S 13.35 9.42
n 100 72

a) at the 0.05 level of significance, is there evidence of a difference in the variability of the computer anxiety experienced by males and females?
b) Interpret the P-Value
c) What assumption do you need to make about the two populations in order to justify the use of the F test?
d) Based on (a) and (b) which t test defined in section 10.1 should you use to test whether there is a significant difference in mean computer anxiety for female and male students?
Determine the upper tail critical values of F in each of the following two-tailed tests:
&#913;) &#945;= 0.10, n1 = 16,n2= 21
B)&#945; = 0.05, n1= 16,n2= 21
C) &#945;= 0.01, n1= 16, n2= 21

Assume that you have a sample of n1=8, with the sample mean of x1=42, and a sample standard deviation of s1=4, and you have an independent sample of n2=15 from another population with a sample mean of X2=34 and a sample mean of S2=5.
A) What is the value of the pooled-variance t stat test statistic for testing the null Ho= &#956;1= &#956;2?
B) In finding the critical value t &#945;/2, how many degrees of freedom are there?
C) Using the level of siginificance ) &#945;=0.01, what is the critical value for a one-tail test of the hypothesis Ho: &#956;1 is <( or equal to) &#956;2 against the alternative H1= : &#956;1 is >( or equal to) &#956;2?
D) What is your statistical decision?