Amphibian populations are in decline worldwide due to the increasing prevalence of ranavirus infections. Herpetologists (those that study amphibians and reptiles) are especially concerned with how ranavirus infections may be affecting Ozark and eastern hellbender populations.

Suppose both populations of hellbenders are known to have ranavirus infections at a rate of 25%. Suppose a random sample of size 118 is taken of the eastern hellbender population and a random sample of size 177 is taken of the Ozark hellbender population. Every hellbender in each sample is tested for ranavirus, and the sample proportions for each of the two samples are calculated.

Required:
Which of the two sample proportions is more likely to exceed 22% ?

Answer:

The sample proportion of size 177 is more likely to exceed 22%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose both populations of hellbenders are known to have ranavirus infections at a rate of 25%.

This means that [tex]\mu = p = 0.25[/tex]

Sample of size 118:

[tex]n = 118, so [tex]s = \sqrt{\frac{0.25*0.75}{118}} = 0.0399[/tex]

Probability of sample proportion above 22%.

This is 1 subtracted by the pvalue of Z when X = 0.22. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.22 - 0.25}{0.0399}[/tex]

[tex]Z = -0.75[/tex]

[tex]Z = -0.75[/tex] has a pvalue of 0.2266

1 - 0.2266 = 0.7734

0.7734% probability that a random sample of size 118 exceeds 22%.

Sample of size 177:

[tex]n = 177, so [tex]s = \sqrt{\frac{0.25*0.75}{118}} = 0.0325[/tex]

Probability of sample proportion above 22%.

This is 1 subtracted by the pvalue of Z when X = 0.22. So

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.22 - 0.25}{0.0325}[/tex]

[tex]Z = -0.92[/tex]

[tex]Z = -0.92[/tex] has a pvalue of 0.1788

1 - 0.1788 = 0.8212

0.8212 = 82.12% probability that a random sample of size 177 exceeds 22%.

82.12% > 77.34%, so the sample proportion of size 177 is more likely to exceed 22%.

The sample proportion that is more likely to exceed 22% is; the sample proportion with a sample size of 177

We are given;

Population proportion; p = 25% = 0.25

Now, in central limit theorem, the formula for standard deviation is;

σ = √(p(1 - p)/n)

For a sample size of 118, we have;

σ = √(0.25(1 - 0.25)/118)

σ = √0.001588983

σ = 0.03986

Similarly, for a sample size of 177, we have;

σ = √(0.25(1 - 0.25)/177)

σ = √0.001059322

σ = 0.032547

Since we want to find which of the two sample proportions will likely exceed 22% which is p₀ = 0.2, we will use the formula;

z = (p₀ - p)/σ

For sample size of 118, we have;

z = (0.22 - 0.25)/0.03986

z = -0.75

From online p-value from z-score calculator, we have;

p-value = 0.7734 or 77.34%

For sample size of 177, we have;

z = (0.22 - 0.25)/0.032547

z = -0.92

From online p-value from z-score calculator, we have;

p-value = 0.8212 or 82.12%

The p-value of the sample of 177 is higher than the p-value for the sample of 118 and so we can say that the sample proportion with a sample size of 177 is more likely to exceed 22%

Read more about Central Limit theorem at; https://brainly.com/question/25800303

f(x)=x-7 and g(x)=2x-3
find f(g(4))

The coordinates of the vertices of triangle ABC are A(9.-10), B(-15, 0), and C(15, 10). A dilation centered at (0, 0) is perfomed on triangle ABC to produce triangle ABC. The coordinates of the vertices of triangle A'B'C' are A' (13.5, -15), B(-22.5, OJ, and C(22.5, 15). Find the scale factor. will mark brainlyst ​

Please help!

Consider matrices A, B, and C.

Which matrix represents (A-B)-C?

PLEASE HELP ASAP 20 POINTS

The newly proposed city park is rectangle shaped. Blake drew a scale drawing of the park and used a scale of 1 cm: 20 ft

1) If the width on the scale drawing of the city park is 25 centimeters, what is the actual width of the park?

A) 250 feet
B) 400 feet
C)500 feet
D)750 feet

2) If the width on the scale drawing of the city park is 25 centimeters and the length is 30 centimeters, what is the actual area of the park?

A) 75,000 ft^2
B) 110,000 ft^2
C) 300,000 ft^2
D) 750,000 ft^2​

solve each equation for given variable
- 12 = 6i- 6

3.

On a coordinate plane, a line segment has P(6,2) and Q(3,8).

Point M lies on PQ and divides the segment so that the ratio

of PM:MQ is 3:2. What are the coordinates of point M?

A. (4.5, 5.0)

B. (5.6, 4.2)

C. (4.8, 4.4)

D. (4.2, 5.6)

How do I find the volume of this pyramid

The Wall Street Journal reported that the median salary for middle-level manager jobs was approximately $85,000 (The Wall Street Journal, August 6, 2013). Suppose that an independent study of middle-level managers employed at companies located in Atlanta, Georgia, was conducted to compare the salaries of managers working at firms in Atlanta to the national average. The following data show the salary, in thousands of dollars, for a 8. sample of 15 middle-level managers.
108 83 106 73 53 85 80 63 67 75 124 55 93 118 77
a. Compute the median salary for the sample of 15 middle-level managers. How does the median for this group compare to the median reported by The Wall Street Journal?
b. Compute the mean annual salary and discuss how and why it differs from the median a. b. computed in part (a).
c. Compute the first and third quartiles.

Classify each number according to its value
5.2×10-4

HELP ITS URGENT!!! May someone PLEASEE help me?

Mori just replaced the showerhead in her bathroom. the old one used 5.75 gallons per minute of water. Her new showerhead uses 2.5 gallons per minute. how many times has much water did Mori's old showerhead use?​

Find the midpoint of the line segiment with the given endpoints. (-9,-7) and (-8,-5)

Given this circle puzzle what would angle 1-12 be? (Geometry)

Can someone help plzzz!!!

1/1-cos x
+
1/1+cos x

Graph the system below and write its solution.
-2x+y=-4
y=1/2x+2

Two chemical plants, one at Macon and one at Jonestown, produce two types of fertilizer, low phosphorus (LP) and high phosphorus (HP). At each plant, the fertilizer is produced in a single production run, so the two types are produced in fixed proportions. The Macon plant produces 1 ton of LP and 3 tons of HP in a single operation, and it charges $600 for what is produced in one operation, whereas one operation of the Jonestown plant produces 1 ton of LP and 1 ton of HP, and it charges $1,000 for what it produces in one operation. If a customer needs at least 100 tons of LP and 180 tons of HP, how many production runs from each plant should be ordered to minimize the cost.

Elena mixes 5 cups of apple juice with with 2 cups of ginger ale to make punch for a party she wants to make 35 cups of punch how much apple juice does she need to buy?​

Can someone explain to me better on identifying linear functions? Like how would I know the difference when identifying them? Are they a function or not?

What is the GCF of a¹²b⁴, a⁴b⁸, a²⁴b¹⁶ and a¹²b²⁰?​

Casper write the algebraic expression 5b + 3.79. I represents the total cost, in dollars, of buying 5 bagels and a container of cream cheese. Identify any variables, coefficients, and termsin the expression.

Is 3.5 and 3.55 a equivalent decimal?​

What is the answer please

I need to know the answer ASAP

Gerber Product's Gerber Mixed Cereal for Baby contains, in each serving, 60 calories and 11 grams of carbohydrates.† Gerber Mango Tropical Fruit Dessert contains, in each serving, 80 calories and 21 grams of carbohydrates.† If you want to provide your child with 340 calories and 75 grams of carbohydrates, how many servings of each should you use?

Rudy correctly solved the equation 10 = 4r.
Which statement describes his solution?
A
The solution is 40 since 10 times 4 equals 40.
The solution is 2.5 since 4 times 2.5 equals 10.
С
The solution is 2.5 since 4 divided by 2.5 equals 10.
D
There is no solution because no value can be multiplied by 4 to get 10.

There are 18 black and 12 navy socks in your drawer. The room is dark and you
cannot turn on the light. What is the least number of socks that you have to take out of
your drawer to be certain that you have a pair of black socks?

a) Work out

16.3-4.97 + 8.6

(2)

I


b) Work out

2164.89 +7

(2)

Why are there so many songs about rainbows
And what's on the other side?
Rainbows are visions, but only illusions
And rainbows have nothing to hide
So we've been told, and some choose to believe it
I know they're wrong, wait and see
Someday we'll find it, the rainbow connection
The lovers, the dreamers, and me
Who said that every wish would be heard and answered
When wished on the morning star?
Somebody thought of that, and someone believed it
Look what it's done so far
What's so amazing that keeps us stargazing
And what do we think we might see?
Someday we'll find it, the rainbow connection
The lovers, the dreamers, and me
All of us under its spell
We know that it's probably magic
Have you been half asleep, and have you heard voices?
I've heard them calling my name
Is this the sweet sound that calls the young sailors?
The voice might be one and the same
I've heard it too many times to ignore it
It's something that I'm supposed to be
Someday we'll find it, the rainbow connection
The lovers, the dreamers, and me
La-da-da, de-da-da-do
La-da-da-da-da-de-da-do

A strawberry farmer will receive 37 per bushel of strawberries during the first week of harvesting each week after that the value will drop 0.8 per bushel the farmer estimates that there are approxiamately 129 of strawberries int he fieldsand that the crop is increasing at a rate of four bushels per week when should the farmer harvest the strawberries to maximize their value? (Assume that "during the first week of harvesting" here means week 1. How many bushels of strawberries will yield the maximum value? (Round your answer to the nearest integer.)
bushels
2. What is the maximum value of the strawberries? (Round your answer to two decimal places.)
$