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

a) See step by step explanation

b) z(s) = - 2.178

c) z(c) = - 1.64

d) We reject H₀

e) The proportion of drivers has decreased

Explanation:

We assume a survey with a random sample

Normality population

Size is big enough to use the approximation of binomial distribution to normal distribution

2019 sample:

sample size n = 963

drivers who admitted going more than 10 miles over the limit

x₁ = 315

p₁ = 315/963 p₁ = 32.71 % or p₁ = 0.3271 and q₁ = 1 - 0.3271

q₁ = 0.6729

Hypothesis Test:

a) Null Hypothesis H₀ p₁ = 36 %

Alternative Hypothesis Hₐ p₁ < 36 % or p₁ < 0.36

b) To calculate z(s) ; z(s) = ( p₁ - 0.36 ) / √ (p₁*q₁)/n

z(s) = ( 0.3271 - 0.36 ) / √ ( 0.3271* 0.6729)/963

z(s) = - 0.0329 / 0.0151

z(s) = - 2.178

c) we will use a confidence interval of 95 %. Then significance level α = 5 % α = 0.05 As the alternative hypothesis indicates we are going to develop a one-tail test

From z- table we find z(c) = - 1.64

d) Comparing z(s) and z(c) |z(s)| > |z(c)|

Then z(s) is in the rejection region for H₀ we reject H₀

e) we can support that the proportion of drivers has decreased since 2002