Respuesta :
Answer:
Null hypothesis: H0 = 0.65
Alternative hypothesis: Ha ≠ 0.65
z = 1.172
P value = P(Z≠1.172) = 0.24
Decision we fail to reject the null hypothesis. That is, there is convincing evidence enough to reject the Null hypothesis.
Rule
If;
P-value > significance level --- accept Null hypothesis
P-value < significance level --- reject Null hypothesis
Z score > Z(at 95% confidence interval) ---- reject Null hypothesis
Z score < Z(at 95% confidence interval) ------ accept Null hypothesis
Step-by-step explanation:
Given;
n=80 represent the random sample taken
Null hypothesis: H0 = 0.65
Alternative hypothesis: Ha ≠ 0.65
Test statistic z score can be calculated with the formula below;
z = (p^−po)/√{po(1−po)/n}
Where,
z= Test statistics
n = Sample size = 80
po = Null hypothesized value = 0.65
p^ = Observed proportion = 57/80 = 0.7125
Substituting the values we have
z = (0.7125-0.65)/√(0.65(1-0.65)/80)
z = 1.17201807734
z = 1.172
To determine the p value (test statistic) at 0.05 significance level, using a two tailed hypothesis.
P value = P(Z≠1.172) = 0.241197 = 0.24
Since z at 0.05 significance level is between -1.96 and +1.96 and the z score for the test (z = 1.172) which falls within the region bounded by Z at 0.05 significance level. And also the one-tailed hypothesis P-value is 0.24 which is higher than 0.05. Then we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that at 5% significance level the null hypothesis is valid.
