Question

You claim you are psychic and can predict a coin flip 60% of the time. To test your claim, your friend has you predict a coin flip and then records whether or not you are correct. You do this 200 times and find you are right 135 times. Considering a null hypothesis that you are correctly predict the coin flip 60% of the time, using a hypothesis test, which of the following statements is most accurate?

a. You cannot reject the null at the 10% level of significance.
b. You can reject the null at the 10% level of significance, but cannot reject the null at the 5%, 2%, or 1% level of significance.
c. You can reject the null at the 10% and 5% level of significance, but cannot reject the null at the 2%, or 1% level of significance.
d. You can reject the null at the 10%, 5%, and 2% level of significance, but cannot reject the null at the 1% level of significance.
e. You can reject the null at the 10%, 5%, 2%, and 1% level of significance

Answer 1

Answer:

You can reject the null at the 10% and 5% level of significance, but cannot reject the null at the 2%, or 1% level of significance. ( D )

Step-by-step explanation:

let : P = 0.6

x = 135 , n = 200

p = 135 / 200 = 0.675

H0 : P = 0.6

Ha : P ≠ 0.6

performing the test statistic = ( 0.675 - 0.6 ) / $\sqrt{\frac{0.60(1-0.60)}{200} }$

= 0.075 / 0.0346 ≈ 2.17

p-value = 2 * P ( Z > - 2.17 )  ( using excel function ; NORMSDIST )

            = 2 * 0.015  = 0.03