Question 1112813: A random sample of 140 observations is selected from a binomial population with unknown probability of success p. The computed value of p^ is 0.61.
(1) Test H0:p≤0.65 against Ha:p>0.65. Use α=0.05.
test statistic z= ?
critical z score ?
The decision is
A. There is sufficient evidence to reject the null hypothesis.
B. There is not sufficient evidence to reject the null hypothesis.
(2) Test H0:p≥0.65 against Ha:p<0.65. Use α=0.05.
test statistic z= ?
critical z score ?
The decision is
A. There is not sufficient evidence to reject the null hypothesis.
B. There is sufficient evidence to reject the null hypothesis.
(3) Test H0:p=0.55 against Ha:p≠0.55. Use α=0.01.
test statistic z= ?
positive critical z score ?
negative critical z score ?
The decision is
A. There is not sufficient evidence to reject the null hypothesis.
B. There is sufficient evidence to reject the null hypothesis.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! 1) standard error(SE) of proportion = square root(0.61 * (1-0.61) / 140) = 0.04
:
test statistic z = (0.65 - 0.61) / 0.04 = 1
:
this is an upper one-tailed test for alpha = 0.05
:
critical z-score = 1.645
:
since the test statistic is < 1.645, we select answer A
:
2) this is a lower one-tailed test
:
test statistic z = 1
critical z-score = -1.645
:
since the test statistic is < 1.645, we select answer B
:
3) this is a two-tailed test, alpha = 0.05/2
:
test statistic z-score = (0.55 - 0.61) / 0.04 = -1.5
:
positive critical z-score = 1.960
negative critical z-score = -1.960
:
since test statistic is > -1.960, we select answer A
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