Mark takes out a $238,000 mortgage for 30 years. Instead of paying his monthly payment of $1,220.09, he decides to pay $1,420.09
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Let X be the length of rulers. X follows Normal distribution with mean μ and standard deviation σ = 0.02. A sample of size n=4 is drawn from population and sample mean m=1000. We have to find 90% confidence interval for population mean μ.
Here population standard deviation is given to us so we will use z confidence interval for mean. It is given as
(Sample mean - Margin of error , Sample mean + Margin of error)
Where margin of error for z confidence interval is
ME = σ
Where σ = population standard deviation = 0.02
n= sample size =4
= Critical z score value for given confidence level
We have to find here 90% confidence interval so confidence level c= 0.9
α = 1 -c =1-0.9 = 0.1
=
=
Here we have to find z score value such that area below it is -z is 0.05 and above z is 0.05
Using excel function to find z score value
=NORM.S.INV(0.05) = -1.645
For calculating confidence interval we consider positive z score value which is 1.645
So the margin of error is
ME =
ME = 0.01645
90% confidence interval for mean is
(Sample mean - ME, Sample mean+ME)
1000- 0.01645, 1000+0.01645
(1000.01645, 999.9836)
Rounding interval upto 3 decimal places
(1000.016, 999.984)
90% confidence interval for population mean is (1000.016, 999.984)
Answer:
See below
Step-by-step explanation:
<h3>Continuation of the question</h3><u>Data in the table:</u>
<u>PH 4 5 6 7 8 9 10 11 </u>
<u>Bacteria 116 120 131 136 141 151 148 163</u>
- <em>Create a scatter plot to represent the data: Based on the data and your scatter plot, what do you think a good linear function would be to represent the data?</em>
<em>See attached for scatter plot</em>
We can see the chart is close to linear function. Let's build one based on data in the table
<u>The line will be in the form of:</u>
- y = mx + b
<u>If we use two points and get the equation</u>
- (4, 116) and (8, 141)
<u>Finding the slope:</u>
- m = (141-116)/(8-4) = 25/4 = 6.25
<u>Then, finding y-intercept:</u>
- 116 = 6.25*4 + b
- b = 116 - 25 = 91
<u>So the line is:</u>
- y = 6.25x + 91
<em>Note: This is approximate best fit graph and it is attached as well. Exact formula for the line is built by using different method and is very close to the one above</em>
