Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the population proportion p at the given level of significance
alphaα
using the given sample statistics.Claim:
pnot equals≠0.24;
alphaαequals=0.10;
Sample statistics:
ModifyingAbove p with caretpequals=0.21,
nequals=200
Can the normal sampling distribution be used?
state the null and alternative hypothesis.
determine the critical value.
find the z-test statistic.
what is the result of the test?
Reject
Upper H 0H0.
The data provide sufficient evidence to support the claim.
B.Fail to reject
Upper H 0H0.
The data do not provide sufficient evidence to support the claim.
C.Reject
Upper H 0H0.
The data do not provide sufficient evidence to support the claim.
D.Fail to reject Upper H 0H0.
The data provide sufficient evidence to support the claim.
E.
The test cannot be performed.
Solution :
This is the two tailed test .
The null and alternative hypothesis is
H0 : p = 0.24
Ha : p 0.24
n = 200
= 0.21
P0 = 0.24
1 - P0 = 1 - 0.24 = 0.76
z = - P0 / [P0 * (1 - P0 ) / n]
= 0.21 - 0.24 / [(0.24 * 0.76) / 200]
= -0.99
Test statistic = -0.99
= 0.10
/ 2 = 0.10 = 0.05
Z/2 = Z0.05 = 1.645
critical value = 1.645
Test statistic > critical value
Reject the null hypothesis .
A) The data provide sufficient evidence to support the claim.
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