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Veronika [31]
3 years ago
10

The Tennessee Tourism Institute (TTI) plans to sample information center visitors entering the state to learn the fraction of vi

sitors who plan to camp in the state. Current estimates are that 35% of visitors are campers. How many visitors would you sample to estimate the population proportion of campers with a 95% confidence level and an allowable error of 2%?
Mathematics
1 answer:
baherus [9]3 years ago
7 0

Answer: 2185

Step-by-step explanation:

Let p be the proportion of visitors are campers.

Given : The Tennessee Tourism Institute (TTI) plans to sample information center visitors entering the state to learn the fraction of visitors who plan to camp in the state.

The prior proportion of visitors are campers : p=0.35

Allowable error : E= 2%= 0.02

We know that the z-value for 95% confidence = z_c=1.96

Then by Central Limit Theorem , the required sample size would be :

n=p(1-p)(\dfrac{z_{c}}{E})^2

\Rightarrow\ n=0.35(1-0.35)(\dfrac{1.96}{0.02})^2\\\\ n= 0.35(0.65)(9604)

Simply , we get

n=2184.91\approx2185  [Rounded to the next whole number.]

Hence, the smallest sample size to estimate the population proportion of campers =2185

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Read 2 more answers
What is the mode and mean for class A and the range and medium for class B????
melamori03 [73]
Hello!

First you have to list the data in both classes

Class A
41, 42, 45, 46, 47, 48, 52, 53, 54, 59, 61, 61, 64, 68, 71, 82, 85, 90

Class B
41, 42, 59, 62, 64, 69, 71, 75, 77, 78, 78, 80, 83, 84, 84, 86, 86, 87, 92, 92, 95
------------------------------------------------------------------------------------------------------
First we are going to find the mode and mean of class A

The mode is the number that appears the most

The number that appears the most is 61

The mode is 61

To find the mean you add all the numbers together and divide the sum by the amount of numbers added

41 + 42 + 45 + 46 + 47 + 48 + 52 + 53 + 54 + 59 + 61 + 61 + 64 + 68 + 71 + 82 + 85 + 90 = 1069

Divide this by the amount of numbers added

1069 / 18 = 59.3888...

The mean is 59.3888

The mode is 61 and the mean is 59.39 for class A
------------------------------------------------------------------------------------------------------
We are going to find the range and median for class B

To find the range you subtract the smallest number from the largest on

The smallest number is 41
The largest number is 95

Subtract these

95 - 41 = 54

The range is 54

To find the median you list the numbers from least to greatest and look for the number in the middle

41, 42, 59, 62, 64, 69, 71, 75, 77, 78, 78, 80, 83, 84, 84, 86, 86, 87, 92, 92, 95

The number in the middle is 78

The range is 54 and the median is 78
------------------------------------------------------------------------------------------------------
Hope this helps!
6 0
3 years ago
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