Posted by **Gayla** on Sunday, June 8, 2008 at 7:35pm.

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.

- Statistics -
**MathGuru**, Tuesday, June 10, 2008 at 10:05am
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.

- Statistics -
**MathGuru**, Tuesday, June 10, 2008 at 10:31am
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!

- Statistics -
**Gayla**, Wednesday, June 11, 2008 at 5:12am
Thank you for your help.

## Answer This Question

## Related Questions

- Statistics - A coin was flipped 60 times and came up heads 38 times. (a) At the...
- Word Problem - A coin was flipped 60 times and came up heads 38 times. (a) At ...
- statistics - A coin was flipped 60 times and came up heads 38 times. (a) At the...
- probability - Suppose an unfair coin comes up heads 52.2% of the time if it is ...
- Statistics - You are shown a coin that its owner says is fair in the sense that ...
- science - A coin will be tossed 15 times, and I have to decide whether it lands ...
- Math - A biased coin is tossed 3 times. The probability that the coin will land ...
- math - In a game, a player tosses a coin 4 times. If the player gets 3 or 4 ...
- Math - Victoria tossed a coin 30 times and got 17 heads. What is the ratio of ...
- Math - "The probability of getting heads on a biased coin is 1/3. Sammy tosses ...

More Related Questions