A random sample of 120120 observations is selected from a binomial population wi
ID: 3175068 • Letter: A
Question
A random sample of 120120 observations is selected from a binomial population with unknown probability of success pp. The computed value of p p^ is 0.770.77. (1) Test H0:p=0.65H0:p=0.65 against Ha:p>0.65Ha:p>0.65. Use =0.01=0.01.
test statistic z=
critical z score =
The final conclusion is A. We can reject the null hypothesis that p=0.65p=0.65 and accept that p>0.65p>0.65.
B. There is not sufficient evidence to reject the null hypothesis that p=0.65p=0.65.
(2) Test H0:p=0.55H0:p=0.55 against Ha:p<0.55Ha:p<0.55. Use =0.01=0.01.
test statistic z
critical z score
The final conclusion is
A. We can reject the null hypothesis that p=0.55p=0.55 and accept that p<0.55p<0.55.
B. There is not sufficient evidence to reject the null hypothesis that p=0.55p=0.55.
(3) Test H0:p=0.55H0:p=0.55 against Ha:p0.55Ha:p0.55. Use =0.05=0.05. test statistic z=z= positive critical zz score negative critical zz score
The final conclusion is
A. There is not sufficient evidence to reject the null hypothesis that p=0.55p=0.55.
B. We can reject the null hypothesis that p=0.55p=0.55 and accept that p0.55p0.55.
Explanation / Answer
Given,
sample size(n)=120
computed p-value(p-)=0.77
A.1) H0: p=0.65
Ha: p>0.65
alpha=0.01
test statistic z=0.77-0.65/sqrt(0.65*0.35/120)
z=2.756
Critical value= 2.58
test statistic z(2.756)>critical value(2.58)
the conclusion is we reject the null hypothesis
A.2) H0: p=0.55
Ha: p<0.55
alpha=0.01
test statistic z=0.77-0.55/sqrt(0.55*0.45/120)
z=4.844
Critical value= 2.58
test statistic z(4.844)>critical value(2.58)
the conclusion is we reject the null hypothesis
A.3) H0: p=0.55
Ha: p0.55
alpha=0.01
test statistic z=0.77-0.55/sqrt(0.55*0.45/120)
z=4.844
Critical value= 2.58
test statistic z(4.844)>critical value(2.58)
the conclusion is we reject the null hypothesis
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