10 13 oup gth 20 23 21 17 16 20 17 16 10 15 12 10 ence in the o-tailed test a. I

Question

10 13 oup gth 20 23 21 17 16 20 17 16 10 15 12 10 ence in the o-tailed test a. Is there a significant difference in reported pain between the two conditions? Use a two-tailed test with = .01. b. Compute Cohen's d to estimate the size of the football and noncontact ead impacts tive perfor- performance port athletes The follow- ts obtained treatment effect. 14. In a classic study in the area of problem solving, Katona (1940) compared the effectiveness of two methods of instruction. One group of participants was shown the exact, step-by-step procedure for solving a problem and was required to memorize the solution. Participants in a second group were encour- aged to study the problem and find the solution on their own. They were given helpful hints and clues, but the exact solution was never explained. The study included the problem in the following figure showing a pattern of five squares made of match- sticks. The problem is to change the pattern into exactly four squares by moving only three matches (All matches must be used, none can be removed, and all the squares must be the same size.) After three weeks, both groups returned to be tested again. The two groups did equally well on the matchstick problem they had learned earlier. But when they were given new problems (similar to the matchstick problem), the memorization group had much lower scores than the group who explored and found the solution on their own. The following data demon- strate this result. thletes 4 10 for the con- athletes? tact of variance

Explanation / Answer

Part a

Solution:

Here, we have to use two sample pooled t test for the population means (assuming equal population variances). The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: There is no any statistically significant difference exists between the performances on new problems for given two groups.

Alternative hypothesis: Ha: There is a statistically significant difference exists between the performances on new problems for given two groups.

H0: µ1 = µ2 Vs Ha: µ1 µ2

This is a two tailed test.

Level of significance or alpha value is given as 0.05 or 5%.

= 0.05

We are given following data:

Var = SS/(n – 1)

SD = sqrt(Var)

Find a solution on our own

Memorization of the solution

n

8

8

M

10.5

6.16

SS

108

116

Var

15.42857143

16.57142857

SD

3.927922024

4.070801957

DF = n1+n2 – 2 = 8 + 8 – 2 = 14

Pooled variance = Sp2 =[ (n1 – 1)*S1^2 + (n2 – 1)*S2^2 ]/[ (n1 + n2 – 2)]

Sp2 = [ (8 – 1)*3.9279^2 + (8 – 1)*4.0708^2] / (8 + 8 – 2)

Sp2 = 15.9999

Test statistic formula is given as below:

t = (X1bar – X2bar) / sqrt[Sp2((1/n1)+(1/n2))]

t = (10.5 - 6.16) / sqrt(15.9999*((1/8)+(1/8)))

t = 2.170006781

P-value = 0.0477 (by using t-table or excel)

P-value < = 0.05

So, we reject the null hypothesis that there is no any statistically significant difference exists between the performances on new problems for given two groups.

There is sufficient evidence to conclude that there is a statistically significant difference exists between the performances on new problems for given two groups.

Part b

Solution:

Here, we have to construct the 90% confidence interval for difference between two population means.

We are given

Population 1 Sample

Sample Size

8

Sample Mean

10.5

Sample Standard Deviation

3.9279

Population 2 Sample

Sample Size

8

Sample Mean

6.16

Sample Standard Deviation

4.0708

Confidence level = 90%

DF = n1+n2 – 2 = 8 + 8 – 2 = 14

Critical t-value = 1.7613 (by using t-table)

Confidence interval = (X1bar – X2bar) -/+ t*sqrt[(S1^2/n1)+(S2^2/n2)]

Confidence interval = (10.5 – 6.16) -/+ 1.7613*sqrt[(3.9279^2/8)+(4.0708^2/8)]

Confidence interval = 4.34 -/+ 3.5226

Lower limit = 4.34 – 3.5226 = 0.8174

Upper limit = 4.34 + 3.5226 = 7.8626

Confidence interval = (0.8174, 7.8626)

Find a solution on our own

Memorization of the solution

n

8

8

M

10.5

6.16

SS

108

116

Var

15.42857143

16.57142857

SD

3.927922024

4.070801957

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