2. A statistics professor has asked his students to flip coins over the years. H

Question

2. A statistics professor has asked his students to flip coins over the years. He has kept track of how many flips land heads and how many land tails. Combining the results of his students over many years, he has formed a 95% confidence interval for the long-run population proportion of heads to be (.497, .513).

a. Why is this interval so narrow?

b. Suppose he were to conduct a hypothesis test of whether the long-run population proportion of heads differs from one-half. Based on this interval (do not conduct the test), would he reject the null hypothesis at the .05 significance level? Explain briefly (no more than one sentence).

c. Does the interval provide strong evidence that the long-run population proportion of heads is much different from one-half? Explain briefly.

Explanation / Answer

a) when the trial is conducted repeatedly for large number of times, then the standard deviation of number of heads become less.

the standard deviation of sampling distribution is = sqrt(pq/n) , where p and q are constant, by increasing the size of n, the sqrt(pq/n) will decrease. Hence this interval become less.

b)No. This interval contains 0.5 so we can't reject the null hypothesis.

c)No. it is not much diferent from one half

If the long run proportion of 0.5 is tested then there is a chance of margin of error due to sampling has to be considered. So the actual value should be with in that margin of error.

here the interval is (0.497, 0.513), This interval contains the value 0.5 so we shouldnt reject the null hypothesis.

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