120 students' preferences for the five Statistics professors at a college are given in the table below. The objective is to conduct a chi-square goodness-of-fit test at α=0.05�=0.05 to determine if there are preferences for some professors. The dean, however, wishes they are liked equally. a. Fill in the missing values in the given table. Professor Observed Frequency f� Expected Frequency e� (f−e)2e(�−�)2� A 25 B 16 C 31 D 21 E 27 Report expected frequencies (e)o 1 decimal place. Report (f−e)2evalues to 3 decimal places. b. The alternate hypothesis is There is no preference for any of the professors There is a preference for some professors c. Calculate the value of the test statistic. χ2=
120 students' preferences for the five Statistics professors at a college are given in the table below. The objective is to conduct a chi-square goodness-of-fit test at α=0.05�=0.05 to determine if there are preferences for some professors. The dean, however, wishes they are liked equally. a. Fill in the missing values in the given table. Professor Observed Frequency f� Expected Frequency e� (f−e)2e(�−�)2� A 25 B 16 C 31 D 21 E 27 Report expected frequencies (e)o 1 decimal place. Report (f−e)2evalues to 3 decimal places. b. The alternate hypothesis is There is no preference for any of the professors There is a preference for some professors c. Calculate the value of the test statistic. χ2=
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120 students' preferences for the five Statistics professors at a college are given in the table below. The objective is to conduct a chi-square goodness-of-fit test at α=0.05�=0.05 to determine if there are preferences for some professors. The dean, however, wishes they are liked equally.
a. Fill in the missing values in the given table.
| Professor | Observed Frequency f� |
Expected Frequency e� |
(f−e)2e(�−�)2� |
|---|---|---|---|
| A | 25 |
|
|
| B | 16 |
|
|
| C | 31 |
|
|
| D | 21 |
|
|
| E | 27 |
|
|
Report expected frequencies (e)o 1 decimal place.
Report (f−e)2evalues to 3 decimal places.
b. The alternate hypothesis is
There is no preference for any of the professors
There is a preference for some professors
c. Calculate the value of the test statistic.
χ2=
Round values to 2 decimal places.
d. What are the degrees of freedom for this test?
d.f.=
e. What is the critical value for this test at α=0.05�=0.05 ?
Critical Value=Critical Value=
Round values to 1 decimal place.
f. Based on these results, the correct decision at α=0.05 is:
Reject H0; there is not enough evidence of preference for some professors.
Do not reject H0; there is not enough evidence of preference for some professors.
Reject H0; there is enough evidence of preference for some professors.
Do not reject H0; there is enough evidence of preference for some professors.
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