Guessing on a True/False Test A true/false test has 50 questions. Suppose a passing grade is 35 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 35 answers correct out of 50. Use a significance level of 0.05. Steps 1 and 2 of a hypothesis test procedure are given. Show steps 3 and 4, and be sure to write a clear conclusion. Step 1: H 0 : p = 0.50 H a : p > 0.50 Step 2: Choose the one-proportion z -test . Sample size is large enough, because n p 0 is 50 0.5 = 25 and n 1 − p 0 = 50 0.50 = 25 , and both are more than 10. Assume the sample is random and α = 0.05.
Guessing on a True/False Test A true/false test has 50 questions. Suppose a passing grade is 35 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 35 answers correct out of 50. Use a significance level of 0.05. Steps 1 and 2 of a hypothesis test procedure are given. Show steps 3 and 4, and be sure to write a clear conclusion. Step 1: H 0 : p = 0.50 H a : p > 0.50 Step 2: Choose the one-proportion z -test . Sample size is large enough, because n p 0 is 50 0.5 = 25 and n 1 − p 0 = 50 0.50 = 25 , and both are more than 10. Assume the sample is random and α = 0.05.
Solution Summary: The author explains the step 3 and 4 for the hypothesis testing and writes the conclusion. The alternative hypothesis shows that the test is right-sided.
Guessing on a True/False Test A true/false test has 50 questions. Suppose a passing grade is 35 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 35 answers correct out of 50. Use a significance level of
0.05.
Steps 1 and 2 of a hypothesis test procedure are given. Show steps 3 and 4, and be sure to write a clear conclusion.
Step 1:
H
0
:
p
=
0.50
H
a
:
p
>
0.50
Step 2: Choose the one-proportion
z
-test
.
Sample size is large enough, because
n
p
0
is
50
0.5
=
25
and
n
1
−
p
0
=
50
0.50
=
25
, and both are more than 10. Assume the sample is random and
α
=
0.05.
Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.
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