A survey was conducted of new students at State U. Students were asked to name w
ID: 3208953 • Letter: A
Question
A survey was conducted of new students at State U. Students were asked to name which of three factors was most important in their decision to attend State U: Tuition, Location or Reputation. Group 1 is first-year students, Group 2 is transfers, and Group 3 is MBAs. Chi-square results are below.
Chi-Square Test: Tuition, Location, Reputation
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
Tuition Location Reputation Total
1 50 40 32 122
42.70 38.95 40.35
1.248 0.029 1.729
2 16 23 20 59
20.65 18.83 19.52
1.047 0.921 0.012
3 25 20 34 79
27.65 25.22 26.13
0.254 1.080 2.370
Total 91 83 86 260
Chi-Sq = 8.690, DF = 4, P-Value = 0.069
1. In the observed data, which factor was chosen most frequently by the first-year students (Group 1) as the most important factor?
2. What should we conclude based on this analysis?
3. Which of the following conclusions makes the most sense, given these results?
4. In this data set, 122 (46.9%) of the 260 students surveyed were first-year students. If the null hypothesis is true, what percentage of students who said that Tuition was the most important factor to them should be first-year students? Use one decimal place.
5. For which group did we observe more students saying that reputation was the most important factor than we expected to pick reputation as the most important factor?
6. Explain what is wrong with the following statement:
The P-value for a chi-square significance test was 1.05.
7. A chi-square test was used to test the null hypothesis that there is an association between two categorical variables.
8. What's wrong with this statement? Expected cell counts are computed under the assumption that the alternative hypothesis is true.
9. What's wrong with this statement?
Chi-square analysis will tell us whether two qualitative variables are correlated.
10. Explain what is wrong with this statement. The chi-square test is useful for explaining the relationship between high school GPA and college GPA.
TuitionExplanation / Answer
Result:
A survey was conducted of new students at State U. Students were asked to name which of three factors was most important in their decision to attend State U: Tuition, Location or Reputation. Group 1 is first-year students, Group 2 is transfers, and Group 3 is MBAs. Chi-square results are below.
Chi-Square Test: Tuition, Location, Reputation
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
Tuition Location Reputation Total
1 50 40 32 122
42.70 38.95 40.35
1.248 0.029 1.729
2 16 23 20 59
20.65 18.83 19.52
1.047 0.921 0.012
3 25 20 34 79
27.65 25.22 26.13
0.254 1.080 2.370
Total 91 83 86 260
Chi-Sq = 8.690, DF = 4, P-Value = 0.069
1. In the observed data, which factor was chosen most frequently by the first-year students (Group 1) as the most important factor?
Tuition
Location
Reputation
2. What should we conclude based on this analysis?
We should fail to reject H0 at the 5% significance level, and reject H0 at the 10% significance level.
We should fail to reject H0 both at the 5% significance level and at the 10% significance level.
We should reject H0 at the 5% significance level, and fail to reject H0 at the 10% significance level.
We should reject H0 both at the 5% significance level and at the 10% significance level.
None of the above answers is correct.
3. Which of the following conclusions makes the most sense, given these results?
There is substantial evidence that the three groups of students picked State U for different reasons.
There is some evidence that the different groups of students picked State U for different reasons, but the evidence is not substantial.
There is no evidence that the different groups of students picked State U for different reasons.
4. In this data set, 122 (46.9%) of the 260 students surveyed were first-year students. If the null hypothesis is true, what percentage of students who said that Tuition was the most important factor to them should be first-year students? Use one decimal place.
42.7*100/260= 16.4
5. For which group did we observe more students saying that reputation was the most important factor than we expected to pick reputation as the most important factor?
First-year
Transfer
MBA
None of these groups
6. Explain what is wrong with the following statement:
The P-value for a chi-square significance test was 1.05.
Units must be provided for the P-value.
The P-value for a chi-square significance test must be negative.
A chi-square test does not provide a P-value.
The P-value must be a number between 0 and 1.
7. A chi-square test was used to test the null hypothesis that there is an association between two categorical variables.
The null hypothesis should be that there is no association between the variables.
A chi-square test does not deal with categorical variables.
A chi-square test deals with more than 2 variables.
The alternative hypothesis must be tested with a test.
8. What's wrong with this statement? Expected cell counts are computed under the assumption that the alternative hypothesis is true.
The observed cells rather then the expected cells are computed under this assumption.
The assumption should be that the null hypothesis is true.
The expected cell counts should be given and not computed.
Computations should always be made with no prior assumptions.
9. What's wrong with this statement?
Chi-square analysis will tell us whether two qualitative variables are correlated.
There is no statistical test for the correlation between two variables.
Chi-square only measures positive correlation, not negative correlation.
Qualitative variables cannot be correlated.
The test only shows that the variables are correlated if we reject H0.
10. Explain what is wrong with this statement. The chi-square test is useful for explaining the relationship between high school GPA and college GPA.
Chi-square analysis can only be used for qualitative variables, and GPAs are quantitative variables.
These variables are not independent, so you can't use chi-square analysis.
The two variables aren't measured at the same point in time, so chi-square analysis doesn't make sense.
The two variables are correlated, and chi-square analysis can only be used with uncorrelated variables.
Tuition
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