Respuesta :
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
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 ± [tex]z^{*}[/tex] [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
Step 1
Find the value of p
p=[tex]\frac{0.584+0.816}{2}[/tex]
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,
[tex]z^{*}[/tex]= 1.96
now substitute the values in the above formula:
[tex]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} }[/tex]
n=59.95 =60
The number of students selected by the teacher were 60
