Question

A Pew Internet survey in 2016 examined several demographic variables of users of ride-hailing apps such as Uber or Lyft, including education, age, race, and income. Of the 4787 adults included in the survey, 2369 were college graduates, of which 687 had used a ride-hailing app. Among the 2418 adults who had not completed college, 268 had used a ride hailing app. Is there good evidence that the proportion of adults who have used a ride-hailing app is different between college graduates and those without a college degree?

a) Check the conditions for inference and report whether they are met

b) State the null and alternative hypotheses

c) Draw a picture of the sampling distribution. Label the mean and your sample statistic (mean difference in sample proportions) and shade the area that corresponds to the alternative hypothesis

d) Find and report the test statistics and p-value

e) Interpret your results using an alpha of your choice

Answer 1

Part a

Both samples are independent. Sample sizes are adequate.

Part b

Null hypothesis: H₀: There is evidence that the proportion of adults who have used a ride-hailing app is same for college graduates and those without a college degree.

Alternative hypothesis: H_a: There is evidence that the proportion of adults who have used a ride-hailing app is different between college graduates and those without a college degree.

H₀: p₁ = p₂ versus H_a: p₁ ≠ p₂

Part c

Required sketch is given as below:

Part d

Test statistic is given as below:

Z = (P1-hat – P2-hat) / sqrt(p-hat*(1 – P-hat)*((1/N1) + (1/N2)))

We are given

X1=687, N1=2369, P1-hat = X1/N1 = 687/2369 = 0.289995779

X2=268, N2=2418, P2-hat = X2/N2 = 268/2418 = 0.110835401

(P1-hat – P2-hat) = 0.289995779 - 0.110835401 = 0.179160378

P-hat = (X1+X2)/(N1+N2) = (687+268)/(2369+2418) = 0.1995

Z = (P1-hat – P2-hat) / sqrt(p-hat*(1 – P-hat)*((1/N1) + (1/N2)))

Z = 0.179160378/ sqrt(0.1995*(1 – 0.1995)*((1/2369) + (1/2418)))

Z = 15.5085

P-value = 0.0000

Critical value = -/+ 1.96

Part e

We have

P-value = 0.0000 < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that there is evidence that the proportion of adults who have used a ride-hailing app is different between college graduates and those without a college degree.