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# Hypothesis Testing of Mean: Independent sample t test

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20. In a classic study of problem solving, Duncker (1945) asked participant to mount a candle on a wall in an upright position so that it would burn normally. One group was given a candle, a book of matches, and a box of tacks. A second group was given the same items, except that the tacks and the box were presented separately as two distinct items. The solution to the problems involves using the tacks to mount the box on the wall, creating a shelf for the candle. Duncker reasoned that the first group of participants would have trouble seeing a "new" function for the box (as a shelf) because it was already serving a function (holding tacks). For each participant, the amount of time to solve the problem was recorded. Data similar to Duncker's are as follows:

Time to solve Problem (in seconds)
Box of tacks
128
160
113
101
94 Tacks and Box separate
42
24
68
35
47

n = 5 n = 5
M = 119.20 M = 43.20
SS = 2746.80 SS = 1066.80

Following the four steps outlined below, test the null hypothesis that there are no significant differences between the two groups.

1) State the null and alternative hypothesis and an alpha level of &#945; = .01, two-tailed, to test the hypothesis (use both the appropriate symbol and words).
2) Calculate the degree of freedom for an independent measure test and locate the critical region (using the provided table; df=df1+df2)
3) Calculate the appropriate t statistic for the problem
4) Make a decision and write an APA-style result section for your findings. (do the data indicate a significant difference between the two conditions)?
Make sure that you show all computations and writer a complete APA result section for the question.

Formula:

df=df1+df2 = (n1-1) + (n2-1)
See attached file for complete list of formulas.