Statistics – Hypothesis Testing

A newspaper article reported that the typical American family spent an average of $81 for Halloween candy and costumes last year. A sample of n=16 families this year produced a mean of $90 with SS = 6000. Do these data indicate a statistically significant increase in spending? Use ?=.05 a. H0 and H1 in words OR symbols b. the t-value you compute c. your decision regarding H0, and d. Results of homogeneity of variance test and effect size, if appropriate e. your APA conclusion based on the results 2) In a classic study of problem solving, Duncker (1945) asked subjects to mount a candle on a wall in an upright position so that it would burn normally. One group of subjects was given a candle, a book of matches, and a box of tacks. A second group was given the same items, except the tacks and the box were presented separately as two distinct items. The solution to this problem involves using the tacks to mount the box on the wall, which creates a shelf for the candle. Duncker reasoned that the first group would have trouble seeing a “new” function for the box (a shelf) because it was already serving a function (holding tacks). For each subject, the amount of time to solve the problem was recorded. The data are as follows: Box of tacks Tacks and box separate 128 42 160 24 113 68 101 35 94 47 SS = 2746.8 SS = 1066.8 Did subjects who were presented the box and tacks separately take significantly less time to solve the problem? Use ?=.05. Indicate: a. a statement of your hypotheses in words OR symbols b. the t-value you compute c. your decision regarding H0 and why, and d. Results of homogeneity of variance test and effect size, if appropriate e. an APA conclusion based on your results 3) A researcher for a cereal company wanted to demonstrate the health benefits of eating oatmeal. A sample of 9 volunteers was obtained and each subject ate a fixed diet without any oatmeal for 30 days. At the end of the 30-day period, cholesterol was measured for each individual. Then the subjects began a second 30-day period in which they repeated exactly the same diet except for 2 cups of oatmeal each day. After the second 30-day period, cholesterol levels were measured again. The scores for the 9 subjects were as follows: Are these data sufficient to demonstrate a significant change in cholesterol level after 30 days with an oatmeal diet? Use ?=.05. Indicate: a. the hypotheses in words b. the statistical hypotheses c. your decision regarding H0 and your conclusion d.Results of homogeneity of variance test and effect size, if appropriate e. calculate and interpret the 95% confidence interval 4) “Achievement test scores are declining all around us,” brooded Professor Probity. “Here are my final exam scores for last year and this year on the same exam.” What did Professor Probity discover? This Year: 29, 27, 26, 22, 19, 15, 14, 10, 10 SS = 425.15 Last Year: 27, 28, 25, 24, 22, 20, 18, 16, 12 SS = 226.42 Indicate: a. a statement of your hypotheses in words b. the t-value you compute c. your decision regarding H0 and why, and d. Results of homogeneity of variance test and effect size, if appropriate e. an APA conclusion based on your results 5) To determine how well people are complying with the posted speed limits, the State Highway Patrol measured automobile speeds on a section of highway where the posted speed limit is 60mph. For a sample of n=100 cars during daylight hours and good weather conditions, they obtained an average speed of = 62mph with SS=2475. a. Make a 95% confidence interval around the sample mean (5 points) b. Does the confidence interval indicate people were speeding and how can you tell?

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