Question

Fair Coin? A coin is called fair if it lands on heads 50% of all possible tosses. You flip a game token 100 times and it comes up heads 41 times. You suspect this token may not be fair.

(a) What is the point estimate for the proportion of heads in all flips of this token? Round your answer to 2 decimal places.


(b) What is the critical value of z (denoted z_α/2) for a 99% confidence interval? Use the value from the table or, if using software, round to 2 decimal places.
z_α/2 =

(c) What is the margin of error (E) for a 99% confidence interval? Round your answer to 3 decimal places.
E =

(d) Construct the 99% confidence interval for the proportion of heads in all tosses of this token. Round your answers to 3 decimal places.
< p <

(e) Are you 99% confident that this token is not fair?

No, because 0.50 is within the confidence interval limits.Yes, because 0.50 is not within the confidence interval limits.    Yes, because 0.50 is within the confidence interval limits.No, because 0.50 is not within the confidence interval limits.

Answer 1

Solution :

Given that,

n = 100

x = 41

a)

Point estimate = sample proportion = = x / n = 0.41

1 - = 0.59

b)

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.58

c)

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.576 * (((0.41 * 0.59) / 100)

= 0.127

d)

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.41 - 0.127 < p < 0.41 + 0.127

0.283 < p < 0.537

e)

Yes, because 0.50 is within the confidence interval limits.