In a random sample of 75 individuals, it was found that 52 of them prefer coffee to tea. What is the margin of error for the tru
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Answer:
0.089
Step-by-step explanation:
f(x) = -ln(x) and g(x) = x²
Start by graphing the region. The two curves intersect at about (0.653, 0.426), with g(x) on the left and f(x) on the right. The region is the triangular area between the curves and above the x-axis.
If we were to cut the region horizontally (perpendicular to the y-axis), the resulting line is the width of the square cross section. The thickness of this square is dy. So the volume of the square is:
dV = A dy
dV = s² dy
dV = (x₂ − x₁)² dy
dV = (e⁻ʸ − √y)² dy
The total volume is the sum of all the squares from y=0 to y=0.426.
V = ∫ dV
V = ∫₀⁰'⁴²⁶ (e⁻ʸ − √y)² dy
Evaluate with a calculator:
V ≈ 0.089
Answer: 1.467
Step-by-step explanation:
Formula of Margin of Error for (n<30):-
Given : Sample size : n= 22
Level of confidence = 0.90
Significance level :
By using the t-distribution table ,
Critical value :
Standard deviation:
Then, we have
Hence, the margin of error for the confidence interval for the population mean with a 90% confidence level =1.467