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Do students at various universities differ in how sociable they​ are? Twenty-five students were randomly selected...

Do students at various universities differ in how sociable they​ are? Twenty-five students were randomly selected from each of three universities in a region and were asked to report on the amount of time they spent socializing each day with other students. The result for University X was a mean of 7 hours and an estimated population variance of 3 hours; for University​ Y, M=6, S2=2; and for University​ Z, M=8, S2=1.5. What should you​ conclude? Use the 0.05 level. Complete parts​ (a) through​ (c) below.

​(a) Use the steps of hypothesis testing.

Determine the null and research hypotheses. Choose the correct answer below.

A.

The null hypothesis is that at least two of these populations have the same mean. The research hypothesis is that the population means are not the same.

B.

The null hypothesis is that the population means are not the same. The research hypothesis is that these populations have the same mean

C.

The null hypothesis is that these populations have the same mean The research hypothesis is that the population means are not the same.

D.

The null hypothesis is that the population means are not the same. The research hypothesis is that at least two of these populations have the same mean.

Determine the characteristics of the comparison distribution for the data.

The comparison distribution will be an F distribution with

dfBetween=

and

dfWithin=

.

Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected for the data.

At the 0.05​ level, the cutoff F is ____

​(Round to two decimal places as​ needed.)

Determine the​ sample's score on the comparison distribution for the data.

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Determine the null and research hypotheses.

option C is right

The null hypothesis is that these populations have the same mean The research hypothesis is that the population means are not the same.

Determine the characteristics of the comparison distribution for the data.

Total groups k= 3

Total students n = 25+25+25=75

df between = k-1=3-1

df within = n-k =75-3 =72

The critical F score is 3.12 ( using excel formula =F.INV.RT(0.05,2,72))

Since the Test statistic F = 11.5384 greater than 3.12, we shall reject the null hypothesis. We have evidence to say that students at various universities differ in how sociable they​ are

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