# A friend has offered to play a gambling game with you

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12.A friend has offered to play a gambling game with you that involves flipping a coin that hehas provided.Since a flip of heads will be to his advantage, you want to test the coin forfairness before you begin to play.Your friend is willing to let you flip the coin 50 times todetermine if the probability of getting heads is actually 0.50, as it should be if the coin is fair.(a) Assume for the moment that the coin is fair.If ˆpis the proportion of heads in 50 flips ofthe coin, what are the mean and standard deviation of the sampling distribution of ˆp?(b) Explain why you can use the formula for the standard deviation of ˆpin this setting.(c)You flip the coin 50 times and get 30 heads.Do you risk insulting your friend byrefusing to play with his coin?Support your answer with an appropriate probabilitycalculation.
326The Practice of Statistics, 4/e- Chapter 7© 2011 BFW Publishers13.Teenagers send many text messages—recent polls cite medians of more than 50 per day.Consider a large population of teenagers for whom the distribution of the number of textmessages sent per day is strongly skewed to the right.Here is the five-number summary fornumber of texts per day for this population:Minimum = 0Quartile 1 = 20Median = 55Quartile 3 = 140Maximum = 250Suppose we take random samples of size 32 from this population and calculate Q1for each ofour samples.Below is a dotplot of Q1from 50 such samples.(a) Briefly explain what the dot at 35 represents.(b) Is the sample Q1an unbiased estimator of the population Q1?Justify your answer.
Test 7BAP StatisticsName:Part 1:Multiple Choice.Circle the letter corresponding to the best answer.1.In a study of the effects of acid rain, a random sample of 100 trees from a particular forest isexamined.Forty percent of the trees show some signs of damage.Which of the followingstatements is correct?
2.The sampling distribution of a statistic is
© 2011 BFW PublishersThe Practice of Statistics, 4/e- Chapter 7327

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