Question

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

Answer 1

Answer:

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).