Chapter 11: Q. 11.84 (page 466)

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.
$x = 3$
$n = 100$
$H_{0} : p = 0.04$
$H_{a} : p \neq 0.04$
$α = 0.10$

Short Answer

Expert verified

(a) The sample proportion is $0.03$

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

Step by step solution

Part (a) Step 1: Given information

The given data is

$n = 100$

x = 3

$H_{0} : p = 0.04$

$H_{a} : p \neq 0.04$

$α = 0.10$

Part (a) Step 2: Explanation

The sample proportion is expressed as

$\hat{p} = \frac{x}{n}$

The sample proportion is calculated as

$\hat{p} = \frac{3}{100}$

$= 0.03$ .

Part (b) Step 1: Given information

The given data is

$x = 3$

$n = 100$

$H_{0} : p = 0.04$

$H_{a} : p \neq 0.04$

$α = 0.10$

Part (b) Step 2: Explanation

Test the hypothesis as

$H_{0} : p = 0.04$

$H_{0} : p \neq 0.04$

Calculate the value of $n p_{0}$

$n p_{0} = (100) (0.04)$

$= 4$

Calculate the value of $n (1 - p_{0})$

$n (1 - p_{0}) = (100) (1 - 0.04)$

$= 100 (0.96)$

$= 96$

Hence, $n p_{0} < 5$

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

Part (c) Step 1: Given information

The given data is

$x = 3$

$n = 100$

$H_{0} : p = 0.04$

$H_{a} : p \neq 0.04$

$α = 0.10$

Part (c) Step 2: Explanation

Because $n p_{0}$ is 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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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.
$x = 3$
$n = 100$
$H_{0} : p = 0.04$
$H_{a} : p \neq 0.04$
$α = 0.10$

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Explanation

Part (b) Step 1: Given information

Part (b) Step 2: Explanation

Part (c) Step 1: Given information

Part (c) Step 2: Explanation

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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=3n=100H0:p=0.04Ha:p≠0.04α=0.10

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Explanation

Part (b) Step 1: Given information

Part (b) Step 2: Explanation

Part (c) Step 1: Given information

Part (c) Step 2: Explanation

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Mechanics Maths

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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.
$x = 3$
$n = 100$
$H_{0} : p = 0.04$
$H_{a} : p \neq 0.04$
$α = 0.10$