Question

Two statistics professors at two rival schools decide to use IQ scores as a measure of how smart the students at their respective schools are. IQ scores are known to be Normally distributed. The two professors will use this knowledge to their advantage. They will randomly select 10 students from their respective schools and determine the students' IQ scores by means of the standard IQ test. The two professors will use the pooled version of the two-sample t test to determine whether the students at the two universities are equally smart. Let m₁ and m₂ represent the mean IQ scores of the students at the two universities. Let s₁ and s₂ be the corresponding population standard deviations. The hypotheses they will test are H₀: m₁ – m₂ = 0 versus H_a: m₁ –m₂ ¹ 0. Based on the two samples of 10 students, the two professors find the following information: = 113,

= 122 s₁ = 8, and s₂ = 12. (Hint: Calculate s_p² first.)

27.	What is the value of the test statistic?
	A)	0.107
	B)	–1.97
	C)	-2.18
	D)	–3.00

28.	Suppose the professors had wished to test the hypotheses H0: m1 = m2 versus Ha: m1 < m2. What can we say about the value of the P-value? (Hint: use df=n1+n2-2.)
	A)	P-value < 0.01
	B)	0.01 < P-value < 0.02
	C)	0.02 < P-value < 0.025
	D)	0.025 < P-value < 0.05

29.	The two professors also wish to test the hypothesis that the groups are equivalent in how variable their IQ scores are. To do this, they wish to test the hypotheses H0: s1 = s2 versus Ha: s1 ¹ s2. What can we say about the value of the P-value?
	A)	P-value < 0.01
	B)	0.01 < P-value < 0.025
	C)	0.025 < P-value < 0.05
	D)	P-value > 0.05

30.	A study compares five groups with ten observations in each group. An F statistic of 3.75 is reported. What are the degrees of freedom for this F statistic?
	A)	4 and 45
	B)	4 and 46
	C)	5 and 10
	D)	5 and 50

31.	A study compares three population means. Three independent samples with 15 observations each are taken. The SSE = 1146 and the SST = 1450. What is the value of the F statistic?
	A)	1.11
	B)	3.32
	C)	4.98
	D)	5.97

32.	A study compares four groups with six observations in each group. How large does the F statistic need to be for rejecting the null hypothesis at the 5% significance level?
	A)	2.53
	B)	2.60
	C)	2.76
	D)	3.10

33.	In a study comparing four groups with six observations in each group, the MSE = 467 and the MSG = 2345. What is the value of the coefficient of determination?
	A)	0.484
	B)	0.516
	C)	0.587
	D)	0.939

34.	A study compares six groups with five observations in each group. An F statistic of 3.712 is reported. What can we say about the P-value for this F test?
	A)	P-value < 0.001
	B)	0.001 < P-value < 0.01
	C)	P-value > 0.01
	D)	0.01 < P-value < 0.05

Answer 1

27 - 28:

For 27 correct option is B.

Since p-value for 2 tailed test is 0.0641 so p-value for one tailed test is 0.0641 / 2= 0.03205.

So for 28 correct option is (D) 0.025 < P-value < 0.05.