A coin is tossed 52 times and 33 heads are observed. Would we infer that this is

Question

A coin is tossed 52 times and 33 heads are observed. Would we infer that this is a fair coin? Use a 95% level confidence interval to base your inference.
The sample statistic for the proportion of heads is: ______ (3 decimals)

The standard error in this estimate is:_________ (3 decimals)

The correct z* value for a 95% level confidence interval is: ______ (3 decimals)

The lower limit of the confidence interval is: ______ (3 decimals)

The upper limit of the confidence interval is: __________ (3 decimals)
Based on this confidence interval, it is  __________plausible  not plausible that the coin is fair.

Explanation / Answer

a. Sample statistic for the proportion of heads = p = 33/52 = .635

b. The standard error in this estimate is SE = Sqrt(p*p'/n) = sqrt(.635*.365/52) = .0667

c. Correct Z* for 95% CI is 1.96 ( this is critical value of Z based on 95% CI)

d. Lower limit is .635 - 1.96*.0667 = .504

e. Upper limit is .635 + 1.96*.0667 = .766

Based on the upper/lower limit based interval, it is NOT plausible that the coin is fair

This is because .5 ( which means a fair coin) DOES NOT LIE between lower and upper limits

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