Question

A truelfalse test has 100 questions. Suppose a passing grade is 60 or more correct answers. Test the claim that a student knows more than half of the answers and is not just guessing. Assume the student gets 60 answers correct out of 100. Use a significance level of 0.05. Steps 1 and 2 of a hypothesis test procedure are given below. Show step 3, finding the test statistic and the p-value and step 4, interpreting the results. Step 1: Ho:p 0.50 Ha p>0.50 Step 2: Choose the one-proportion z-test. Sample size is large enough, because npo is 100(0.5)-50 and n (1-Po) -100(5)-50, and both are more than 10. Assume the sample is random Step 3: Compute the z-test statistic, and the p-value z(Round to two decimal places as needed.) p-value(Round to three decimal places as needed.) Step 4: Do you reject or not reject the null hypothesis? What does this mean in the context of the data? A. Reject Ho-The probability of doing this well by chance alone is not small enough to conclude that the student is not guessing. O B. Do not reject Ho. The probability of doing this well by chance alone is so small that it can be concluded that the student is not guessing. ° C. Do not reject Ho. The probability of doing this well by chance alone is not small enough to conclude that the student is not guessing. O D. Reject Ho. The probability of doing this well by chance alone is so small that it can be concluded that the student is not guessing. Click to select your answer(s).

Answer 1

Sample proportion is 0.60,

The standard deviation of the sampling distribution of proportions is

$Se=\sqrt { 0.50(1-0.50)\over 100}=0.05$

So the value if the test static is

$z={ 0.60-0.50\over 0. 05}=2$

Now the test is right tailed test

So p-value is

Since 0.0228<0.05

So reject the null hypothesis

Option D is correct