Last school year, the student body of a local university consisted of 30% freshm

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Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification: freshmen 83, sophomores 68, juniors 85, and seniors 64. The school superintendent is interested in determine whether or not there has been a significant change in the classification between last school year and this school year. The expected number of freshmen is

Select one:

A. 83

B. 30

C. 90

D. 10

E. None of the above answers is correct

Question 5

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Reference student body problem statement above, which of the following is a correct statement if the hypothesis to be tested at the 5% level of significance?

Select one:

A. the null hypothesis should state that the classification for this school year is independent of last school year classification

B. the alternative hypothesis should state that the classification for this school year is independent of last school year classification

C. the null hypothesis should be pfreshmen=0.30, psophomores=0.24, pjuniors=0.26 , pseniors=0.20

D. the alternative hypothesis should be pfreshmen=0.30, psophomores=0.24, pjuniors=0.26, pseniors=0.20

E. None of the above answers is correct

Question 6

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Reference student body problem statement above, what is the critical value(s) from the table if the hypothesis to be tested at the 5% level of significance?

Select one:

A. 1.645

B. 1.96

F. 7.815

G. 5.99

H. None of the above answers is correct

Question 7

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Reference student body problem statement above, what specific conclusion should be drawn based on the value of the test statistic and its critical value?

Select one:

A. there isn't enough information provided to answer this question

B. the classification for this school year is independent of last school year classification

C. the classification for this school year is dependent on last school year classification

D. there has been a significant change in the classification from last school year to this school year

E. there has not been a significant change in the classification from last school year to this school year

Question 8

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Reference student body problem statement above and the specific conclusion drawn (the answer to the last multiple choice question), what percentage of times the conclusion drawn is the wrong conclusion?

Select one:

A. there isn't enough information to answer this question

B. 100%

C. 0%

D. 50%

E. 5%

F. 95%

G. None of the above answers is correct

Question 9

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Select one:

A. true

B. false

Explanation / Answer

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification: freshmen 83, sophomores 68, juniors 85, and seniors 64. The school superintendent is interested in determine whether or not there has been a significant change in the classification between last school year and this school year. The expected number of freshmen is

There are 300 students and 30% are freshmen, so

0.30*300 = 90. [OPTION C]

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OPTION C. the null hypothesis should be pfreshmen=0.30, psophomores=0.24, pjuniors=0.26 , pseniors=0.20 [ANSWER]

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As this is a chi^2 test of fit, and there are 4 groups, hence df = 4 - 1 = 3. At 0.05 level, using table/technology,

chi^2(crit) = 7.815 [ANSWER, F]

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Doing an observed/expected value table,          
O   E   (O - E)^2/E  
83   90   0.544444444  
68   72   0.222222222  
85   78   0.628205128  
64   60   0.266666667  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    1.661538462      

As chi^2 < 7.815, then we do not Reject Ho:

OPTION E. there has not been a significant change in the classification from last school year to this school [ANSWER]

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As we didn't reject Ho, then the probability of a type I error is

OPTION E: 5% [ANSWER]

***************************

FALSE. [ANSWER]

It can only take nonnegative values.

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