Mathematics, 05.05.2020 05:46, yourmumsanoodle

In a population of bats living in a certain region, 30 percent have a wingspan greater than 10 inches. In a random sample of 80 bats living outside of the region, 20 has a wingspan greater than 10 inches. Consider a one-sample z-test to investigate whether there is evidence that the proportion of bats with a wingspan greater than 10 inches living outside the region is different from that of the bats living in the region. Which of the following is the correct test statistic?

a. z= 0.30 - 0.25/ √ (0.25)(0.75)/80

b. z= 0.30 - 0.25/ √ (0.30)(0.70)/80

c. z= 0.20 - 0.30/ √ (0.30)(0.70)/80

d. z= 0.25 - 0.30/ √ (0.25)(0.75)/80

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answered: janilaw1

The correct static test is $z = \frac{0.30-0.25}{\sqrt{\frac{0.30 (0.70)}{80} } }$ .

Given that ;

Number of persons living in certain region have a wingspan greater than 10 inches = p_o =30% = 0.30

In a random sample of n= 80 bats living outside of the region, 20 has a wingspan greater than 10 inches.

To determine whether there is any difference between the proportion of bats with a wingspan greater than 10 inches living outside the region from that of the bats living in the region.

According to the question ;

A one-sample z-test to investigate ,

The hypothesis can be defined as follows:

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

$p = \frac{20}{80}$

H₀: There is no difference between the proportion of bats with a wingspan greater than 10 inches living outside the region and of the bats living in the region.

= p - p₀ = 0.

Hₐ: There is a difference between the proportion of bats with a wingspan greater than 10 inches living outside the region and of the bats living in the region.

= p - p₀ ≠ 0.

n = 80 , X = 20 , p₀ = 0.30

A z-test for single proportion will be used to perform the analysis.

The sample proportion of bats living outside of the region having a wingspan greater than 10 inches as follows:

The test statistic is ,

$z = \frac{p-p_o}{\sqrt{\frac{p_0 (1-p_0)}{n} } }$

$z = \frac{0.25-0.30}{\sqrt{\frac{0.30 ( 1-0.30)}{80} } }$

The correct test statistic is $z = \frac{0.30-0.25}{\sqrt{\frac{0.30 (0.70)}{80} } }$ .

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answered: Sushmitarai4934

The correct option is (e).

Step-by-step explanation:

In this case we need to determine whether there is any difference between the proportion of bats with a wingspan greater than 10 inches living outside the region from that of the bats living in the region.

The hypothesis can be defined as follows:

H₀: There is no difference between the proportion of bats with a wingspan greater than 10 inches living outside the region and of the bats living in the region, i.e. p - p₀ = 0.

Hₐ: There is a difference between the proportion of bats with a wingspan greater than 10 inches living outside the region and of the bats living in the region, i.e. p - p₀ ≠ 0.

The information provided is:

n = 80

X = 20

p₀ = 0.30

A z-test for single proportion will be used to perform the analysis.

Compute the sample proportion of bats living outside of the region having a wingspan greater than 10 inches as follows:

$p=\frac{X}{n}=\frac{20}{80}=0.25$

The test statistic is given as follows:

$z=\frac{p-p_{0}}{\sqrt{\frac{p_{0}(1-p_{0})}{n}}}$

Compute the value of the test statistic as follows:

$z=\frac{p-p_{0}}{\sqrt{\frac{p_{0}(1-p_{0})}{n}}}$

$=\frac{0.25-0.30}{\sqrt{\frac{0.30(1-0.30)}{80}}}$

$=\frac{0.25-0.30}{\sqrt{\frac{0.30\times 0.70}{80}}}$

Thus, the test statistic is $z=\frac{0.25-0.30}{\sqrt{\frac{0.30\times 0.70}{80}}}$ .

The correct option is (e).

answered: Guest

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answered: Guest

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step-by-step explanation: