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Tom [10]
3 years ago
15

Based on the responses a 95 percent confidence interval for the proportion of all students at the school who would respond yes t

o the question was calculated as (0.584, 0.816) how many students were in the sample selected by the environmental science teacher?
Advanced Placement (AP)
2 answers:
yan [13]3 years ago
8 0

Answer:

The sample size is 60

Explanation:

Using the standard formula for a confidence interval, the interval (0.584 to 0.186) is found by using the formula:

p ± z^{*} \sqrt{\frac{p(1-p)}{n} }

Step 1

Find the value of p

p=\frac{0.584+0.816}{2}

p=0.7

Step 2

Calculate the margin of error

Margin of error= 0.816-0.7

                       = 0.116

Step 3

Using the above formula, calculate the sample size, i.e value of n

Since its a two tailed test, the critical value of z for 95% confidence level is 1.96,

z^{*}= 1.96

now substitute the values in the above formula:

1.96\sqrt{\frac{0.7(1-0.7)}{n} } =0.116\\n=\frac{1.96^{2} (0.7)(1-0.7) }{0.116^{2} }

n=59.95 =60

The number of students selected by the teacher were 60

Serga [27]3 years ago
7 0

Answer:

Number of students ; 60

Explanation:

Using the formula for p +- z * Sqrt ( pq/n )

Let us first calculate the Margin of Error

= 0.816 –0.7 = 0.116

•z* = 1.96

P = (0.584 + 0.116 ) = 0.7

Q = 1- p = 1 – 0.7 = 0.3

Now inserting the values in the formula; we get

0.116 = 1.96 x sqrt { ( 0.7 x 0.3) / n }

Solving the above equation

N = 60 (rounded off to nearest number)

Hence the number of students that were selected by the environmental teacher in the sample is 60

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