A person claims to be able to predict the outcome of flipping a coin. Their clai

Question

A person claims to be able to predict the outcome of flipping a coin. Their claim will be accepted if they can predict the outcomes of flipping a coin on average with a higher percentage that would occur by change, guessing (50%). Upon performing the experiment, the person is correct 18 out of 25 times. Answer the following questions based upon the above experiment.

What is the point estimate for the proportion of times the person predicted the coin flips correctly?
Enter answer as a fraction or a 2 place decimal with a zero to the left of the decimal point. Do not enter your answer in percent.

What is the sample size being used for calculating a confidence interval for the proportion of heads demonstrated base upon the reported data? Enter answer as an integer.

Compute a 95% confidence interval for the proportion of times the person predicted the coin flips correctly. Enter the lower number and the upper number for the confidence interval with the lower number first. Enter answer as a decimal rounded to 3 decimal places with a zero to the left of the decimal point. Do not enter your answer in percent.

What conclusion can you draw from the confidence interval about the ability of the person to predict the outcome of a coin flip?

Select the correct answer and enter the letter that is associated with that answer.

a. Based upon the data, the calculated conference interval supports the claim that the person flipping the coins can predict the outcomes.
b. Based upon the data, the calculated conference interval does not support the claim that the person flipping the coins can predict the outcomes.
c .There is insufficient information to draw any conclusion from the experimental results

What number must the lower number in the confidence interval exceed in order for the confidence interval to support the claim of being able to predict the outcome of flipping a coin?

Enter answer to 1 decimal place with a 0 to the left of the decimal point.

Explanation / Answer

here x=18=number of heads correctly

n=25=number of trial

What is the point estimate for the proportion of times the person predicted the coin flips correctly?

p=x/n=18/25=0.72

here we want to test null hypothesis H0:P=0.5 and alternate hypothesis H1:P>0.5

SE(p)=sqrt(P(1-P)/n=sqrt(0.5*(1-0.5)/25)=0.1

(1-alpha)*100% confidence interval for population proportion =0.72 ±z(alpha/2)*SE(p)

95% confidence interval =0.72±z(0.05/2)*0.1=0.72±1.96*0.1=0.72±0.196=(0.524,0.916)

since P=0.5, does not belong to this interval , so we reject the null hypothesis.

the right choice is a. Based upon the data, the calculated conference interval supports the claim that the person flipping the coins can predict the outcomes.

alternatively

we use z-test and z=(p-P)/SE(p)=(0.72-0.5)/sqrt(0.5*(1-0.5)/25)=2.2

one tailed critical z(0.05)=1.645 is less than calcuated z=2.2, so we fail to accept H0 and conclude that Their claim is accepted.

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