A. <.or=50 B. >220 C.<.50 D.>.50 2.State your decision rule. Fail to Reject H0 i
ID: 3154454 • Letter: A
Question
A. <.or=50
B. >220
C.<.50
D.>.50
2.State your decision rule. Fail to Reject H0 if Z is?
A. >2.33
B. <2.58
C. <-1.65
D. <2.33
3.What is the calculated Z value? Z=?
A.2.0
B.1.20
C.20
D.6.25
4.What is your statistical decision on H0?
A.Fail to reject Ho
B.cannot determine
C.reject Ho
D.need to conduct another sample
5.At the 1 % level of significance does the evidence indicate that more than 50% of the homes in the city are watching American Idol?
A. no
B.cannot determine
C. yes
D. less than 50% are watching
6. What is the p-value?
A. .1151
B.approximately 0
C..1056
D..0228
Explanation / Answer
Here we have to test the hypothesis that,
H0 : p = 50% = 0.5 VS H1 : p > 0.5
where p is population proportion.
q = 1 - p = 1 - 0.5 = 0.5
1. State the alternate hypothesis.
D) H1:>.50
2.State your decision rule. Fail to Reject H0 if Z is?
B. <2.58
Here 2.58 is critical value found by using EXCEL.
syntax is,
=NORMSINV(probability)
where probability = 1 - a/2
a = 0.01
We get critical value is 2.58.
Reject H0 at 1% level of significance if Z > 2.58.
And fail to reject H0 at 1% level of significance if Z < 2.58.
3.What is the calculated Z value?
Test statistic Z = (p^ - p) / sqrt((pq)/n)
p^ is sample proportion = x/n = 220 / 400 = 0.55
Z = (0.55 - 0.5) / sqrt((0.5*0.5) / 220) = 0.05 / 0.025 = 2
Option a) is correct.
4.What is your statistical decision on H0?
Z < 2.58
fail to reject H0 at 1% level of significance.
Option a) is correct.
5.At the 1 % level of significance does the evidence indicate that more than 50% of the homes in the city are watching American Idol?
No
At the 1% level of significance there is not sufficient evidence to say that more than 50% of the homes in the city are watching American Idol.
6. What is the p-value?
P-value we can find by using EXCEL.
syntax is,
=1 - NORMSDIST(z) the test is right sided
where z is test statistic value.
P-value = 0.0228
D..0228
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