Mathematics, 11.03.2020 23:07 erykp17

Mortgage rates: Following are interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia for one day. It is reasonable to assume that the population is approximately normal. 4.751 4.373 4.177 4.676 4.425 4.228 4.125 4.251 3.951 4.192 4.291 4.414 Send data to Excel Part: 0 / 2 Part 1 of 2 (a) Construct a 98% confidence interval for the mean rate. Round the answer to at least four decimal places. A 98% confidence interval for the mean rate is

Answers: 3

Show answers

Answers

Answer from: alejachico2

98% Confidence interval: (4.144 ,4.498)

Step-by-step explanation:

We are given the following in the question:

4.751, 4.373, 4.177, 4.676, 4.425, 4.228, 4.125, 4.251, 3.951, 4.192, 4.291, 4.414

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where x_i are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{51.854}{12} = 4.321$

Sum of squares of differences = 0.5602

$s = \sqrt{\dfrac{0.5602}{11}} = 0.226$

98% Confidence interval:

$\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}$

Putting the values, we get,

$t_{critical}\text{ at degree of freedom 11 and}~\alpha_{0.02} = \pm 2.718$

$4.321 \pm 2.718(\frac{0.226}{\sqrt{12}} ) = 4.321 \pm 0.1773 = (4.144 ,4.498)$

Answer from: haily13

98% confidence interval for the mean rate = [4.1437 , 4.4983]

Step-by-step explanation:

We are given the interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia for one day ;

4.751, 4.373, 4.177, 4.676, 4.425, 4.228, 4.125, 4.251, 3.951, 4.192, 4.291, 4.414

Now, Firstly we will find Mean of above data, Xbar ;

Mean, Xbar = $\frac{\sum X}{n}$ = $\frac{4.751 +4.373+ 4.177+ 4.676+ 4.425+ 4.228+ 4.125 +4.251 +3.951 +4.192+ 4.291 +4.414}{12}$ = 4.321

Standard deviation, s = $\sqrt{\frac{\sum (X-Xbar)^{2} }{n-1} }$ = 0.226

Now, the pivotal quantity for 98% confidence interval for the mean rate is;

P.Q. = $\frac{Xbar-\mu}{\frac{s}{\sqrt{n} }}$ ~ t_n_-_1

where, Xbar = sample mean

s = sample standard deviation

n = sample size = 12

So, 98% confidence interval for the mean rate, $\mu$ is ;

P(-2.718 < t_1_1 < 2.718) = 0.98

P(-2.718 < $\frac{Xbar-\mu}{\frac{s}{\sqrt{n} }}$ < 2.718) = 0.98

P(Xbar - 2.718 * ${\frac{s}{\sqrt{n} }}$ < $\mu$ < Xbar + 2.718 * ${\frac{s}{\sqrt{n} }}$ ) = 0.98

98% confidence interval for $\mu$ = [Xbar - 2.718 * ${\frac{s}{\sqrt{n} }}$ , Xbar + 2.718 * ${\frac{s}{\sqrt{n} }}$ ]

= [4.321 - 2.718 * ${\frac{0.226}{\sqrt{12} }}$ , 4.321 + 2.718 * ${\frac{0.226}{\sqrt{12} }}$ ]

= [4.1437 , 4.4983]

Therefore, 98% confidence interval for the mean rate = [4.1437 , 4.4983]

Answer from: Quest

Whose mistake? can you give more details to what the question is asking?

Answer from: Quest

.24

step-by-step explanation:

the probability is .24

the first player had the highest probability of getting a silver marble

the game could be made fair by adding back the marble that was drawn after each draw

Another question on Mathematics

Mathematics, 21.06.2019 15:30

Sunday: 1 1 2 monday: 1 tuesday: 2 1 2 wednesday: 1 3 4 thursday: 2 friday: 1 1 2 saturday: 2 jenna is a swimmer and trains every day. the schedule shown outlines the number of hours she trains each day. what is the total number of hours that jenna trains during the week?

Answers: 3

Answer

Mathematics, 21.06.2019 20:00

Write the expression as a single natural logarithm. 2 in a - 4 in y

Answers: 1

Answer

Mathematics, 21.06.2019 22:30

Reinel saves 30% of every pay check. his paycheck last week was 560$. how much did reniel save last week?

Answers: 2

Answer

Mathematics, 22.06.2019 00:00

Tony is charged $ 50 and additional $0.15 per miles for renting a car. a) represent the cost of renting a car with an equation,and the determine the cost if he drove it70 miles.b) what would be the cost of a car rental if the car was driven 250 miles? show work

Answers: 1

Answer

You know the right answer?

Mortgage rates: Following are interest rates (annual percentage rates) for a 30-year fixed rate mort...

Questions

Mathematics, 03.05.2020 13:53

Can someone help me with this...

Mathematics, 03.05.2020 13:53

A right triangle has side lengths 5, 12, and 13 as shown below. Use these lengths to find tan A, sin A, and cos A....

Mathematics, 03.05.2020 13:53

The rectangle below has an area of x2 – 16 square meters and a width of x + 4 meters....