scale Question 2. (Based on textbook [IPS] Exercise 8.82) A survey of 1102 teens
ID: 3333876 • Letter: S
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scale Question 2. (Based on textbook [IPS] Exercise 8.82) A survey of 1102 teens collected data about video game use by teens. Part of the data are as follows Genre Percent who play Racing Puzzle Sports 72 74 68 (Participants may select more than one genres they play) (a) Construct a two-sided symmetric 90% confidence interval for estimating the population proportion of sports game players, using normal approximation (b) Based on the data, can we reasonably perform a two sample test that we learned in lecture to compare the proportions of racing and puzzle game players? If yes, what assumptions do we rely on; if no, what is(are) the concern(s)? (Hint: the assumption(s) that we need for performing the two sample proportion test is a subset of the assumptions needed by the two sample t-procedure.) Question 3. Researchers examined the time in minutes before an insulating luid lost its insulating property. The following data are the breakdown times for eight samples of the fluid, which had been randomly allocated to receive one of to voltages of electricity: Times (min) at 26 kV: 5.79 1579.52 2323.70 Times (min) at 28 kV: 68.8 108.29 110.29 426.07 1067.60 (a) Form two new variables by taking the logarithms of the breakdown times: 3 Yi = log(breakdown time at 26kV) and Y2 = log(breakdown time at 28kV). (b) By hand, compute the difference in averages of the log-transformed data: h- (c) Take the antilogarithm of the estimate in (b): et-2, What does this estimate? (See theExplanation / Answer
Question2
Number of surveyed teens = 1102
Sports players = 68
Proportion of players who played sports p^ = 68/1102 = 0.0617
90% confidence interval = p^ +- Z90% sqrt[p^ * (1-p^)/ N]
90% confidence interval = 0.0617 +- 1.645 * sqrt[0.0617 * 0.9383/1102]
90% confidence interval = 0.0617 - 1.645 * 0.007248
= (0.0498, 0.0736)
(b) There are some assumptions that must be followed.
In this case, samples are not independent. As, a person can only be Racing or sports so this is not independent in nature. THis two given values are derived from same set of persons. So, we cannot conduct hypothesis testing for two sample proportions here.
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