Respuesta :
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:
[tex]p=\frac{X}{n}=\frac{20}{80}=0.25[/tex]
The test statistic is given as follows:
[tex]z=\frac{p-p_{0}}{\sqrt{\frac{p_{0}(1-p_{0})}{n}}}[/tex]
Compute the value of the test statistic as follows:
[tex]z=\frac{p-p_{0}}{\sqrt{\frac{p_{0}(1-p_{0})}{n}}}[/tex]
[tex]=\frac{0.25-0.30}{\sqrt{\frac{0.30(1-0.30)}{80}}}[/tex]
[tex]=\frac{0.25-0.30}{\sqrt{\frac{0.30\times 0.70}{80}}}[/tex]
Thus, the test statistic is [tex]z=\frac{0.25-0.30}{\sqrt{\frac{0.30\times 0.70}{80}}}[/tex].
The correct option is (e).
The correct static test is [tex]z = \frac{0.30-0.25}{\sqrt{\frac{0.30 (0.70)}{80} } }[/tex].
Given that ;
Number of persons living in certain region have a wingspan greater than 10 inches = [tex]p_o[/tex]=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:
[tex]p = \frac{x}{n}[/tex]
[tex]p = \frac{20}{80}[/tex]
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 ,
[tex]z = \frac{p-p_o}{\sqrt{\frac{p_0 (1-p_0)}{n} } }[/tex]
[tex]z = \frac{0.25-0.30}{\sqrt{\frac{0.30 ( 1-0.30)}{80} } }[/tex]
The correct test statistic is[tex]z = \frac{0.30-0.25}{\sqrt{\frac{0.30 (0.70)}{80} } }[/tex].
For more information about Simple proportion click the link given below.
vvhttps://brainly.in/question/13350804
