Question

Whenever you are asked to test a hypothesis, be sure to: (a) state the null and alternative hypotheses; (b) state the relevant sample statistic; (c) give the rejection region; (d) compute the test; (e) give your decision and a conclusion in English.

1. Assume that last year, licensed American drivers drove an average of 10,000 miles, with a standard deviation of 2,000 miles (these are population figures). This year, the government campaigned to get people to save gas by driving less. To test the effectiveness of the campaign, a study is conducted. A sample of 100 drivers is drawn at random from the general population and the number o fmiles driven by each person is recorded. On the average, these 100 drivers drove 11,000 miles. Was the campaign effective? Use alpha = .01.

Answer 1

a.) Hypotheses are:

Null: The average driving remain same at 10000 miles

Ho: = 10000

Alternate: The average driving is decreased from 10000 miles after campaign

H1: < 10000

b.)

Since population standard deviation is given and sample size > 30, z-statistic can be used

c.)

Given = 0.01

The test is left tailed test

Critical value of z-statistic is -2.33 at = 0.01

Hence rejection is Z < -2.33

d.)

Given,

n = 100

= 11000

= 2000

z = ( - ) / ( / )

z = 1000 / (2000/10)

z = 1000/200

z = 5

e.)

Since z > -2.33, we fail to reject the Null Hypotheses

This means that average number of miles driven has not decreased when compared to last year.