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a. Determine the sample proportion.

b. Decide whether using the one-proportion z-test is appropriate.

c. If appropriate, use the one-proportion z-test to perform the specified hypothesis test.

x=3

n=100

H0:p=0.04

Ha:p≠0.04

α=0.10

Short Answer

Expert verified

(a) The sample proportion is 0.03

(b) It is not appropriate to use one proportion z-test.

(c) The required hypothesis test as well as the one proportion z-test cannot be carried out.

Step by step solution

01

Part (a) Step 1: Given information

The given data is

n=100

x=3

H0:p=0.04

Ha:p≠0.04

α=0.10

02

Part (a) Step 2: Explanation

The sample proportion is expressed as

p^=xn

The sample proportion is calculated as

p^=3100

=0.03.

03

Part (b) Step 1: Given information

The given data is

x=3

n=100

H0:p=0.04

Ha:p≠0.04

α=0.10

04

Part (b) Step 2: Explanation

Test the hypothesis as

H0:p=0.04

H0:p≠0.04

Calculate the value ofnp0

np0=(100)(0.04)

=4

Calculate the value ofn1-p0

n1-p0=(100)(1-0.04)

=100(0.96)

=96

Hence, np0<5

Therefore, it is not appropriate to use one proportion z-test.

05

Part (c) Step 1: Given information

The given data is

x=3

n=100

H0:p=0.04

Ha:p≠0.04

α=0.10

06

Part (c) Step 2: Explanation

Because np0is fewer than 5, the required hypothesis cannot be tested, and only one proportion z-test can be done.

As a result, the required hypothesis test as well as the one proportion z-test cannot be carried out.

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