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This question is incomplete, the complete question;
The American Psychological Associated conducted a survey in 2003 of psychologists to estimate the average incomes for psychologists based on their academic degree and years of experience. 36 psychologists responded who had a just received their masters degree in 2003. The average was $48,800 with a standard deviation of $16,800.
The 95% Confidence Interval is ($, $ )
Answer:
at 95%, confidence interval is ( $43312, $54288 )
Step-by-step explanation:
Given the data in the question;
sample size n = 36
mean x' = 48,800
standard deviation σ = 16,800
at 95% confidence level;
∝ = 1 - 95% = 1 - 0.95 = 0.05
∝/2 = 0.05 / 2 = 0.025
z critical value, = 1.96
now, confidence interval for population mean is given by the formula
x' ± ( σ/√n )
so we substitute
⇒ 48800 ± 1.96( 16800/√36 )
⇒ 48800 ± 1.96( 2800 )
⇒ 48800 ± 5488
⇒ 48800 - 5488, 48800 + 5488
⇒ ( 43312, 54288 )
Therefore, at 95%, confidence interval is ( $43312, $54288 )
When y=0,
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![\\ \\ ={ \left[ -\frac { { 2x }^{ 2+1 } }{ 2+1 } -\frac { 5{ x }^{ 1+1 } }{ 1+1 } +3x \right] }_{ -3 }^{ \frac { 1 }{ 2 } }](https://tex.z-dn.net/?f=%5C%5C%20%5C%5C%20%3D%7B%20%5Cleft%5B%20-%5Cfrac%20%7B%20%7B%202x%20%7D%5E%7B%202%2B1%20%7D%20%7D%7B%202%2B1%20%7D%20-%5Cfrac%20%7B%205%7B%20x%20%7D%5E%7B%201%2B1%20%7D%20%7D%7B%201%2B1%20%7D%20%2B3x%20%5Cright%5D%20%20%7D_%7B%20-3%20%7D%5E%7B%20%5Cfrac%20%7B%201%20%7D%7B%202%20%7D%20%20%7D)
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Answer: 343/24 units squared.
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Answer: 343/24 units squared.