Question

1. Which of the following sets of data provides the clearest difference between the two samples?

One sample has M = 20 with s2 = 5 and the other has M = 30 with s2 = 5.

One sample has M = 20 with s2 = 5 and the other has M = 25 with s2 = 5.

One sample has M = 20 with s2 = 10 and the other has M = 30 with s2 = 10.

One sample has M = 20 with s2 = 10 and the other has M = 25 with s2 = 10.

2. An independent-measures research study uses two samples, each with n = 10, to compare two treatments. If the results are evaluated with a t statistic using a two-tailed test with a = .05, then the critical region would have boundaries of ____.

t = ±2.101

t = ±2.262

t = ±2.086

t = ±2.093

3. Two samples, each with n = 6 subjects, produce a pooled variance of 20. Based on this information, the estimated standard error for the sample mean difference would be ____.

√(20/5+20/5)

20/6

√(20/6+20/6)

20/12

4. An independent-measures research study uses two samples, each with n = 8 participants. If the data produce a t statistic of t = 2.10, then which of the following is the correct decision for a two-tailed hypothesis test?

Reject the null hypothesis with a = .05 but fail to reject with a = .01.

Reject the null hypothesis with either a = .05 or a = .01.

cannot answer without additional information

Fail to reject the null hypothesis with either a = .05 or a = .01.

5. The results of an independent-measures research study are reported as "t(5) = -2.12, p > .05, two tails." What statistical decision was made?

The researcher failed to reject H0.

There was a marginally significant effect.

cannot be determined from the researcher's statement

The null hypothesis was rejected.

Answer 1

1) For clearest difference between two sample difference between two sample should be large and and their corresponding variances should be small.

Correct option (A) One sample has M = 20 with s2 = 5 and the other has M = 30 with s2 = 5

2) For two tailed test :

DF=n1+n2-2=10+10-2=18

alfa=0.05

From t table :

t critical=t_0.05/2,18 =  ±2.101

t = ±2.101

3) Correct option :C)√(20/6+20/6)

4)Here df=8+8-2=14

t₀ =2.1

P value =tdist(2.1,14,2)= 0.0543

Since p value is larger than both a=0.05 and a=0.01

So

Fail to reject the null hypothesis with either a = .05 or a = .01

Correct option (D)

5) Here p > .05 So researcher failed to reject H0

Correct option (A)