Answer:
Null hypothesis: H0 = 0.50
Alternative hypothesis: Ha > 0.50
z = 1.414
P value = P(Z<-3.16) = 0.0787
Decision: not enough evidence to reject the null hypothesis. Accept null hypothesis.
Not more than half of all drivers drive a car made in this country
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= 200 represent the random sample taken
Null hypothesis: H0 = 0.50
Alternative hypothesis: Ha > 0.50
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 = 200
po = Null hypothesized value = 0.50
p^ = Observed proportion = 110/200 = 0.55
Substituting the values we have
z = (0.55-0.50)/√{0.50(1-0.50)/200}
z = 1.414
z = 1.414
To determine the p value (test statistic) at 0.05 significance level, using a one tailed hypothesis.
P value = P(Z>1.414) = 0.0787
Since z at 0.05 significance level is between -1.96 and +1.96 and the z score for the test (z = 1.414) which falls within the region bounded by Z at 0.05 significance level. And also the one-tailed hypothesis P-value is 0.0787 which is greater than 0.05. Then we can conclude that we don't have enough evidence to FAIL or reject the null hypothesis, and we can say that at 5% significance level the null hypothesis is valid.
