Q1 and Q2 Steven Schmidt 1994 conducted a series of experime

Q1 and Q2: Steven Schmidt (1994) conducted a series of experiments examining the effects of humor on memory. In one study, participants were given a mix of humorous and non-humorous sentences and significantly more humorous sentences were recalled. However, Schmidt argued that the humorous sentences were not necessarily easier to remember, they were simply preferred when participants had the choice between the two types of sentence. To test this argument, he switched to an independent measures design in which one group got a set of exclusively humorous sentences and another group got a set of exclusively non-humorous sentences. The following data are similar to the results from the published independent measures study:

Q1) Use the dataset above to calculate each of the following statistics. Note that the Humorous Sentences Group is the sample for Population 1 and the Non-Humorous Sentences Group is the sample for Population 2. (Show all work starting with formulas).

a) Xbar₁ and Xbar₂

b) df₁ df₂ df_total

c) ?² 1   ?²₂   ?²pooled (estimated population variances)

d) standard error of the sampling distribution

Q2) (This question is related to Q1 so I cannot submit it separately) Your statistics professor is considering changing the amount of humor used in his/her lectures, but is not sure whether this will impact students’ memory for the lecture material. Use the statistics calculated in Q1 to perform a hypothesis test using an independent samples t test with an alpha level of .05 and a two-tailed design (show all 5 steps of hypothesis testing). As part of your results, make a recommendation about whether your statistics professor should use humor in his/her lectures to ensure that students will remember the content. (Show all work starting with formulas)

Scoring Rubric

Problem 1a:

Deduct as follows:

Incorrect Sample 1 mean (1 point)

Incorrect Sample 2 mean (1 point)

Problem 1b:

Deduct as follows:

Incorrect df₁ (1 point)

Incorrect df₂ (1 point)

Incorrect df_total (1 point)

Problem 1c:

Deduct as follows:

If correct pooled variance equation is not used (2 point)

If correct pooled variance value is not found (1 point)

Problem 1d:

Deduct as follows:

If correct equation is not used (1 point)

If correct value is not found (1 point)

Problem 1e:

Deduct as follows:

If correct equation is not used (1 point)

If correct value is not found (1 point)

Problem 2 (12 points):

1.)State the hypothesis

Deduct as follows:

A.If any aspect of null hypothesis written in words is incorrect, be sure students are specifically

naming the IV and DV (.5 point)

B.If any aspect of null hypothesis written in notation is incorrect (.5 point)

C.If any aspect of alternative hypothesis written in words is incorrect, be sure students are specifically

naming the IV and DV (.5 point)

D.If any aspect of alternative hypothesis written in notation is incorrect (.5 point)

2.)Calculate standard error

Deduct as follows:

A.If correct value is not found per Question 1 (1 points)

3.)Determine critical value

Deduct as follows:

A. If the critical value is not correct (1 points)

4.)Conduct hypothesis test

Deduct as follows:

A.If correct t test equation is not used (1 points)

B.If correct t statistic is not found (1 points)

C.If t obtained is not compared to t critical in some form – words or notation (1 point)

5.) Make decision about rejecting/failing to reject the hypothesis

Deduct as follows:

A.If student does not explicitly state either “reject the hypothesis” or “fail to reject the null hypothesis” (1 point)

B.If student does not write correct conclusion in words (1 points)

C.If student does not write correct conclusion in notation (1 points)

D.If student does not correctly apply their results by making a decision about incorporation of humor into the professor’s lectures (2 points)

Humorous Sentences	Non-Humorous Sentences
4	6
5	3
2	5
4	3
6	3
7	4
6	2
6	6
2	4
5	3
4	4
3	4
3	5
3	2
5	6
3	4

Solution

Q1)

a)

Calculating the means of each group,              
              
X1 =    4.25          
X2 =    5.25       [answer]

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b)

df1 = n1 - 1 = 16-1 = 15
df2 = n2 - 1 = 16-1 = 15
dftot = df1 + df2 = 30 [answer]

*************************  
c)
              
Calculating the standard deviations of each group,              
              
s1 =    1.527525232          
s2 =    4.626013402          
              
Thus, the pooled standard deviation is given by              
              
Sigmapooled = sqrt[((n1 - 1)s1^2 + (n2 - 1)(s2^2))/(n1 + n2 - 2)]               
              
As n1 =    16   , n2 =    16  
              
Then              
              
Sigmapooled =    3.444802849          
              
Thus,

sigma1^2 = 2.333333334
sigma2^2 = 21.4
sigmapooled^2 = 11.86666667 [answer]

**************************

d)

Thus, the standard error of the difference is              
              
Sd = S sqrt (1/n1 + 1/n2) =    1.217921727   [answer]

********************************      
e)
              
As ud = the hypothesized difference between means =    0   , then      
              
tobtained = [X1 - X2 - ud]/Sd =    -0.821070827   [answer]  
              
*******************************

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