Recent revenue shortfalls in a southern state led to a reduction in the state bu
ID: 3289646 • Letter: R
Question
Recent revenue shortfalls in a southern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 20% tuition increase. It was determined that such a large increase was needed to simply compensate for lost support from the state. Random samples of 100 freshmen, 100 sophomores, 100 juniors, and 100 seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university's budget at current levels. The results are given in the following table. Strongly opposed Freshman Sophomore Junior Senior Yes 78 72 58 36 No 22 28 42 64 Suppose we wish to test the null hypothesis that there is no association between student year in school and student opinion. Under the null hypothesis, what is the expected number of strongly opposed juniors?
a) 58 b) 84 c) 61 d) 75
Recent revenue shortfalls in a southern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 20% tuition increase. It was determined that such a large increase was needed to simply compensate for lost support from the state. Random samples of 100 freshmen, 100 sophomores, 100 juniors, and 100 seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university's budget at current levels. The results are given in the following table. Strongly opposed Freshman Sophomore Junior Senior Yes 78 72 58 36 No 22 28 42 64 The chi-square statistic for these data equals 43.9. The P-value is
a) greater than 0.10. b) less than 0.01. c) between 0.05 and 0.10. d) between 0.01 and 0.05.
Recent revenue shortfalls in a southern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 20% tuition increase. It was determined that such a large increase was needed to simply compensate for lost support from the state. Random samples of 100 freshmen, 100 sophomores, 100 juniors, and 100 seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university's budget at current levels. The results are given in the following table. Strongly opposed Freshman Sophomore Junior Senior Yes 78 72 58 36 No 22 28 42 64 The chi-square statistic for these data equals 43.9. What conclusion should be drawn from this chi-square test?
a) There is strong evidence that year in school and opposition to the tuition increase are positively correlated.
b) There is no evidence that year in school and opposition to the tuition increase are related.
c) There is some evidence that year in school and opposition to the tuition increase are positively correlated.
d) There is strong evidence that year in school and opposition to the tuition increase are dependent.
Explanation / Answer
applying chi square test on above data:
expected number of strongly opposed juniors =61 option C
chi-square statistic for these data equals =43.9
for above test stat and (n-1=3) degree of freedom p value = b) less than 0.01.
d) There is strong evidence that year in school and opposition to the tuition increase are dependent.
please revert for any clarificaiton required.
Observed O freshman Sophomore Juniors Seniors Total Yes 78 72 58 36 244 No 22 28 42 64 156 Total 100 100 100 100 400 Expected E=rowtotal*column total/grand total freshman Sophomore Juniors Seniors Total Yes 61.000 61.000 61.000 61.000 244 No 39.000 39.000 39.000 39.000 156 Total 100 100 100 100 400 chi square =(O-E)^2/E freshman Sophomore Juniors Seniors Total Yes 4.738 1.9836 0.1475 10.2459 17.115 No 7.410 3.103 0.231 16.026 26.769 Total 12.148 5.086 0.378 26.272 43.884Related Questions
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