Perform the following hypothesis test of a proportion:
HO: p = 0.33
HA: p not equal to 0.33
The sample proportion is 0.31 based on a sample size of 100. Use a 10% significance level.
A) What is the value of the test statistic? (Give answer rounded to 2 decimals) (be careful to make sure your + or - sign is correct)
B) What is the p-value for the problem?
C) should the null hypothesis be rejected? YES or NO
Solution :
This is the two tailed test .
The null and alternative hypothesis is
H0 : p = 0.33
Ha : p 0.33
= 0.31
n = 100
P0 = 0.33
1 - P0 = 0.67
Test statistic = z
= - P0 / [P0 * (1 - P0 ) / n]
= 0.31 - 0.33 / [(0.33 * 0.67) / 100]
= -0.43
P(z < -0.43) = 0.3336
P-value = 2 * 0.3336 = 0.6672
= 0.10
P-value >
Fail to reject the null hypothesis .
No
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