A coin was flipped 60 times and came up heads 38 times. (a)at the .10 level of significance, is the coin biased towards heads? Show your decision rule and calculations. (b) calculate a p-value and interpret it.

Answer 1

Here might be one way to do this problem:

Null hypothesis is that the coin is fair. Ho: p = .5
Alternate hypothesis is that the coin is unfair. Ha: p not equal to .5

Using the binomial formula: P(x) = (nCx)(p^x)[q^(n - x)]
...where n = number of coin tosses, x = number of times came up heads, p = probability given in the null hypothesis, q = 1 - p.

Using your data:
P(60) = (60C38)(.5^38)(.5^22)
= .0123 (rounded to four decimal places)

If the alternate hypothesis uses "not equal to" then we multiply the results by 2. Therefore, 2 * .0123 = .0246
If the alternate hypothesis would have shown a specific direction, then we could have used .0123 as is.

Reject the null hypothesis if the test statistic above is less than .10 level of significance; otherwise, do not reject null.
The p-value is .0246 (the p-value is the actual level of the test statistic). You should be able to take it from here.

I hope this will help.

Answer 2

Correction (this does not change the outcome):

Using the binomial formula: P(x) = (nCx)(p^x)[q^(n - x)]
...where n = number of coin tosses, x = number of times came up heads, p = probability given in the null hypothesis, q = 1 - p.

Using your data:
P(38) = (60C38)(.5^38)(.5^22)
= .0123 (rounded to four decimal places)

*** Changed P(60) to P(38). Sorry for any confusion!

Answer 3

Thank you for your help.