Answered: In a survey of 490 drivers from the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

In a survey of

490

drivers from the South,

409

wear a seat belt. In a survey of

340

drivers from the Northeast,

291

wear a seat belt. At

α=0.05,

can you support the claim that the proportion of drivers who wear seat belts is greater in the South than in the Northeast? Assume the random samples are independent. Complete parts (a) through (e).

(a) Identify the claim and state

and

Ha.

The claim is "the proportion of drivers who wear seat belts in the South is

greater than

the same as

less than

different than

in the Northeast."

Let

represent the population proportion for the South, and

represent the population proportion for the Northeast. State

and

Ha.

Choose the correct answer below.

H0:

p1≤p2

Ha:

p1>p2

H0:

p1≠p2

Ha:

p1=p2

H0:

p1≥p2

Ha:

p1<p2

H0:

p1=p2

Ha:

p1≠p2

H0:

p1>p2

Ha:

p1≤p2

H0:

p1<p2

Ha:

p1≥p2

(b) Find the critical value(s) and identify the rejection region(s).

The critical value(s) is(are)

1.651.65.

(Use a comma to separate answers as needed. Type an integer or a decimal. Round to two decimal places as needed.)

Identify the rejection region(s). Select the correct choice below and fill in the answer box(es) within your choice. (Round to two decimal places as needed.)

z<nothing

and

z>nothing

z>1.651.65

z<nothing

nothing<z<nothing

z=nothing

(Round to two decimal places as needed.)

(d) Decide whether to reject or fail to reject the null hypothesis.

Choose the correct answer below.

Fail to reject

because the test statistic

in the rejection region.

Reject

because the test statistic

is not

in the rejection region.

Reject

because the test statistic

in the rejection region.

Fail to reject

because the test statistic

is not

in the rejection region.

(e) Interpret the decision in the context of the original claim.

Choose the correct answer below.

At the

significance level, there is

insufficient

evidence to support the claim.

At the

significance level, there is

insufficient

evidence to reject the claim.

At the

significance level, there is

sufficient

evidence to support the claim.

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