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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.
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?