Question

2. [EXCEL] Karl Duncker’s results on his ‘Candle Problem’ were published posthumously in 1945. Participants were asked to mount a candle on a wall in an upright position so that it would burn normally. One group of participants was given a candle, a book of matches, and a box full of tacks. A different, independent group of participants were given the same items, except that the box and the tacks were presented separately. The solution is to use the tacks to nail the box to the wall, put the candle in the box and use the matches to light it. Functional fixedness is the idea that people in the first group will take longer to solve the problem, because they will have difficulty seeing a function for the box as a shelf different from its current use as a container. For each participant, the amount of time to solve the problem in seconds was recorded. We want to test whether there is sufficient evidence that the first group took longer to solve the problem. Data similar to Duncker’s is given in the “Question 2” tab in the file “DataAssignment4.xlsx”.

Box of Tacks	Tacks and Box Separate
120	43
146	24
160	68
81	35
95	47
135	45
115	42
131	50
175	37
140	49
87	41
92	48
90	39
132	34
87	27
137	51
96	52
151	43
94	43
158	46
88
112
137
149
92

(a) Define the parameter to be tested. (b) State the null and alternative hypothesese you would use. (c) Use Excel to find the sample size, mean, and standard deviation of each sample. (d) Would you use a pooled or unpooled test? Why? (e) Get the output table from Excel for the hypothesis test. (f) Add a row under your output clearly stating the observed value of your test statistic and your p-value. Write a sentence explaining whether there is sufficient evidence at the α = 0.01 significance level that participants who were given a box of tacks took longer to solve the problem.

Answer 1

The detailed solution is given below

Hypothesis testing to check if the variance are equal

e) Get the output table from Excel for the hypothesis test. (f) Add a row under your output clearly stating the observed value of your test statistic and your p-value. Write a sentence explaining whether there is sufficient evidence at the α = 0.01 significance level that participants who were given a box of tacks took longer to solve the problem

Put the data in excel and go to DATA -> Data Analysis -> t test Two sample Assuming unequal variance

Update the values as shown

Output will be generated as follows

Done by hand to help you understand better