Question

According to government documents in 2002, the percentage of individuals who admitted to consistently going more than 10 miles per hour on the interstate was 36%. A survey conducted in 2019, showed that out of 963 participants surveyed, 315 of them admitted to consistently going more than 10 miles over the speed limit. Is there sufficient evidence at that the percentage of individuals speeding more than 10 miles per hour over the speed limit has decreased since 2002?

a.) What are the null and alternative hypotheses?

b.) What is the value of the test statistic?

c.) What is the critical value?

d.) What is the decision?

e.) What is the conclusion?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.36
Alternative Hypothesis, Ha: p < 0.36

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.3271 - 0.36)/sqrt(0.36*(1-0.36)/963)
z = -2.13

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

Reject H0

There is sufficient evidence to conclude that the percentage of individuals speeding more than 10 miles per hour over the speed limit has decreased since 2002