Question

five years ago, it was estimated that only 5% of new car buyers considered buying an electric vehicle, to see if this percentage has increased a new survey was conducted. a random sample of 200 car buyers revealed that 14 of 200 surveyed said they had considered buying an electric car. You have a significance level of 0.05

1) Find the test statistic and p-value by hand. Draw the appropriate distribution and label the test statistic and p-value.

Answer 1

To Test :-

H0 :- P = 0.05

H1 :- P > 0.05

n = 200
P = X / n = 14/200 = 0.07

Test Statistic :-


Z = 1.30

Test Criteria :-
Reject null hypothesis if

Z < Z_{\alpha} = 1.2978 < 1.6449, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = P ( Z > 1.2978 )
P value = 0.0972
Reject null hypothesis if P value <
Since P value = 0.0972 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is insufficient evidence to support the claim that increased in the percentage of buying new electric car.