Question

# At a school rally, a group of sophomore students organized a free raffle for prizes. They...

At a school rally, a group of sophomore students organized a free raffle for prizes. They claim that they put the names of all the students in the school in the basket and they randomly drew 36 names out of the basket. Of the prize winners, 6 were freshmen, 14 were sophomores, 9 were juniors and 7 were seniors.

The results do not seem that random to you. You think it is a little fishy that sophomores organized the raffle and also won most of the prizes. Your school is composed of 30% freshman, 25% sophomores, 25% juniors, and 20% seniors.

To support your suspicion you decide to perform the following Hypothesis test at a 10% significance level.

 School Population Freshman Sophomore Junior Senior Total Percent of students .30 .25 .25 ,20 100 Expected prize winners A B C D 36 Observed prize winners 6 14 9 7 36

The number of freshman students expected to win a raffle prize is 'A':

1) Enter the numerical value for 'A' as decimal rounded to 1 decimal place.

2) The Null Hypothesis is:

a) The number of students that win raffle prizes is in agreement with the proportion of students at each academic level, Freshman, Sophomore, Junior and Senior.

b) The number of students that win raffle prizes is not in agreement with the proportion of students at each academic level, freshman, sophomore, junior and senior.

Enter answer by selecting the appropriate letter.

3) The Alternate Hypothesis is:

a) The number of students that win raffle prizes is in agreement with the proportion of students at each academic level, freshman, sophomore, junior and senior.

b) The number of students that win raffle prizes is not in agreement with the proportion of students at each academic level, freshman, sophomore, junior and senior.

Enter answer by selecting the appropriate letter.

4) The appropriate distribution for performing the Hypothesis Test is?

a) Uniform Distribution

b) Normal Distribution

c) t Distribution

d) Chi Square Distribution

e) F Distribution

5) What is the critical value of the Test Statistic?

Enter answer rounded to 2 or 3 decimal places. (Chi Square table can be found in LEO-Content-Statistical Resources.)

6)What is the numerical value of the Test Statistic?

Enter the answer rounded to 2 decimal places.

7) The Pvalue is: Enter answer rounded to 3 decimal places with a zero to the left of the decimal point. Do not enter answer as a percent.

8)Your decision based upon running the Hypothesis Test is:

a) Do not reject the Null Hypothesis. The number of students that win raffle prizes is in agreement with the proportion of students at each academic level, freshman, sophomore, junior and senior.

b) Reject the Null Hypothesis. The number of students that win raffle prizes is not in agreement with the proportion of students at each academic level, freshman, sophomore, junior and senior.

Solution:

The number of freshman students expected to win a raffle prize is 'A':

2) The Null Hypothesis is:

Answer: a) The number of students that win raffle prizes is in agreement with the proportion of students at each academic level, Freshman, Sophomore, Junior and Senior.

3) The Alternate Hypothesis is:

Answer: b) The number of students that win raffle prizes is not in agreement with the proportion of students at each academic level, freshman, sophomore, junior and senior.

4) The appropriate distribution for performing the Hypothesis Test is?

5) What is the critical value of the Test Statistic?

Answer: The chi-square critical value at 0.10 significance level for degrees of freedom = 4-1=3 is

6)What is the numerical value of the Test Statistic?

7) The P-value is:

8)Your decision based upon running the Hypothesis Test is:

Answer: a) Do not reject the Null Hypothesis. The number of students that win raffle prizes is in agreement with the proportion of students at each academic level, freshman, sophomore, junior and senior.