A claim was made that 60% of the adult population thinks that there is too much

Question

A claim was made that 60% of the adult population thinks that there is too much violence on television and a random sample of size n = 100 was drawn from this population to check whether that is indeed true. The people in the sample were asked: do you think ther is too much violence on TV? Yes or No? 56% of the people in the sample said Yes.

a) What is the approximate distribution p^ assuming that the claim of 60% is accurate. State its family name, its mu and its standard deviation. Note: p^ = X/n where X is binomial random variable. Statisticians call p^ the sample proportion of successes.

b) What is the probability that p^ is less than 0.56? Is that smaller or larger than 0.05?

c) If the distribution above represents all the possible values of p^ that could occur by chance if the true p is 0.6, do you think that a value of p^ smaller than 0.56 has high probability of having happened by chance?

Explanation / Answer

a) Since the sample size is greater than 30, the distribution is a normal distribution.

mu=p hat=0.6

sd=sqrt(phat(1-phat))/n=0.04899

b) P(p<0.56) = use NORM.DIST(0.56,0.6,0.04899,true) in excel and we get 0.207109. This is larger than 0.05

c) here mu-3*sd=0.453031, hence there is around 99% chance to this occuring. Here we use the normal probability rule.

c)

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