Question

A package delivery service wants to compare the proportion of on-time deliveries for two of its major service areas. In City A, 348 out of a random sample of 425 deliveries were on time. A random sample of 281 deliveries in City B showed that 211 were on time.

1. Calculate the difference in the sample proportion for the delivery times in the two cities.

p̂CityA−p̂CityB =

2. Calculate the pooled estimate of the sample proportion.

p̂ =

3. Calculate the test statistic for this hypothesis test.

=

4. Calculate the p-value for this hypothesis test.

p-value =

5. Compute a 90% confidence interval for the difference p̂CityA−p̂CityB

( , )

Answer 1

The statistical software output for this problem is:

Hence,

1. Difference = 0.0679

2. Pooled estimate = (348 + 211)/(425 + 281) = 0.7918

3. Test statistic = 2.1761

4. p - value = 0.0296

5. 90% confidence interval:

(0.0155, 0.1203)