Question

(06.01 HC)

Football team members suspect the coin used for the coin toss at the beginning of their games is unfair. They believe it turns up tails more often than it should if it were fair. The coach of the team decides to flip the coin 100 times and count the number of tails. His trial results in 55 tails. He decides to carry out a significance test. What is the p-value he obtains and the general conclusion that can be made at a 95% significance level? (4 points)

a	The p-value is 0.159. He should reject the null in favor of the alternative.
b	The p-value is 0.159. He should fail to reject the null.
c	The p-value is 0.841. He should reject the null in favor of the alternative.
d	The p-value is 0.841. He should fail to reject the null.
e	There is not enough information provided to calculate the p-value and make a conclusion.

(06.01 LC)

What conditions must be met to use z procedures in a significance test about a population proportion? (4 points)

I. The sample size is greater than 30.
II. The population is greater than 10 times the sample size.
III. The probability of success multiplied by the sample size is greater than or equal to 10, and the probability of failure multiplied by the sample size is greater than or equal to 10.

a	I only
b	II only
c	III only
d	I and II only
e	II and III only

Answer 1

Solution-1:

Ho:p=0.5

Ha;p>0.5

alpha=0.05

p^=x/n=55/100=0.55

use ti 83 cal

STATS>TESTS>1-PROPZTEST

z=1

p=0.1587

P>0.05

Fail to reject Ho

b	The p-value is 0.159. He should fail to reject the null.

MARK OPTION B

Solution-2:

conditions for hypothesis testing for proportion

Random

Normality(n shpuld be greater than 30)

np^>=10

n(1-p^)>=10

Independence(N/n>10)

population is ten times as large as sample

II. The population is greater than 10 times the sample size.
III. The probability of success multiplied by the sample size is greater than or equal to 10, and the probability of failure multiplied by the sample size is greater than or equal to 10.

MARK OPTION E

e

II and III only