Question

The records of a state-owned company indicate that of all vehicles undergoing emissions testing during the previous year, 70% passed on the first test. A random sample of 200 cars tested in the country during the current year reveals that 62% passed the initial test. Does this data suggest that the true proportion for this country is less than the previous countrywide proportion? Test the relevant hypothesis at the 5% level of significance.

(a) State the null and alternative hypotheses for the test.

(b)What is the test statistic?

(c) Calculate the value of the test statistic for this test.

(d) Determine the critical region(s) for this test.

(e) State the conclusion of this test. Give a reason for your answer.

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.7
Alternative Hypothesis, Ha: p < 0.7

b)

This is asingle proportion z test

c)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.62 - 0.7)/sqrt(0.7*(1-0.7)/200)
z = -2.47

d)
Rejection Region
This is left tailed test, for α = 0.05
Critical value of z is -1.64.
Hence reject H0 if z < -1.64

e)

As the value of test statistic, z is inside critical value range, reject the null hypothesis