You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. From a random sample of 40 business​ days, the mean closing price of a certain stock was ​$108.50 . Assume the population standard deviation is​$11.36 . The​ 90% confidence interval is ​(nothing ​,nothing ​).​(Round to two decimal places as​ needed.) The​ 95% confidence interval is ​(nothing ​,nothing ​). ​(Round to two decimal places as​ needed.) Which interval is​ wider? Choose the correct answer below. The​ 95% confidence interval The​ 90% confidence interval Interpret the results. A. You can be​ 90% confident that the population mean price of the stock is outside the bounds of the​90% confidence​ interval, and​ 95% confident for the​ 95% interval. B. You can be certain that the population mean price of the stock is either between the lower bounds of the​ 90% and​ 95% confidence intervals or the upper bounds of the​ 90% and​ 95% confidence intervals. C. You can be​ 90% confident that the population mean price of the stock is between the bounds of the​ 90% confidence​interval, and​ 95% confident for the​ 95% interval. D. You can be certain that the closing price of the stock was within the​ 90% confidence interval for approximately 36 of the 40 ​days, and was within the​ 95% confidence interval for approximately 38 of the 40 days.

Answer:

The​ 90% confidence interval is ($105.55,$111.45)

The 95% confidence interval is ($104.98,$112.02)

The 95% confidence interval is wider.

C. You can be​ 90% confident that the population mean price of the stock is between the bounds of the​ 90% confidence​interval, and​ 95% confident for the​ 95% interval.

Step-by-step explanation:

90% confidence interval:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.645\frac{11.36}{\sqrt{40}} = 2.95[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 108.50 - 2.95 = $105.55

The upper end of the interval is the sample mean added to M. So it is 108.50 + 2.95 = $111.45

The​ 90% confidence interval is ($105.55,$111.45)

95% confidence interval:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96\frac{11.36}{\sqrt{40}} = 3.52[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 108.50 - 3.52 = $104.98

The upper end of the interval is the sample mean added to M. So it is 108.50 + 3.52 = $112.02

The 95% confidence interval is ($104.98,$112.02)

Which interval is​ wider?

The 95% confidence interval has a larger margin of error, so it is wider.

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

So the correct interpretation is:

C. You can be​ 90% confident that the population mean price of the stock is between the bounds of the​ 90% confidence​interval, and​ 95% confident for the​ 95% interval.

HELPPPP PLZ. I NEED HELP PLZ I WILL GIVE MORE POINTS AND BRAINLIEST FOR CORRECT ANSWER.

Here are the noon temperatures (in degrees Celsius) in a particular Canadian city on Thanksgiving Day for the 10 years from 2002 through 2011: 0, 3, 6, 8, 2, 9, 7, 6, 4, 5. Describe the typical temperature and the amount of variation to a person who has never had a course in statistics. Give three ways of describing the representative temperature and two ways of describing its variation, explaining the differences and how you figured each. (You will learn more if you try to write your own answer first, before reading our answer at the back of the book.)

Russell is purchasing a $175,000 home with a 30-year mortgage. He will put
down $15,000 down payment. Use the table below to find his monthly PMI
payment
Base-To-Loan %
Fixed-Rate Loan
30 yrs. 15 yrs.
ARM 2% + 1 Year Cap
30 yrs.
15 yrs.
95.01% to 97%
0.90% 0.79%
n/a
n/a
90.01% to 95%
0.78% 0.26%
0.92%
0.81%
85.01% to 90%
0.52% 0.23%
0.65% 0.54%
85% and Under
0.32% 0.19%
0.37% 0.26%
O A. $97.50
B. $1170
O c. $1248
O D. $104.00

~!!!! HELP IM IN 7TH GRADE LEARNING 9TH AND 8TH PLEASE HELP !!!!~
QUESTION~
The graph of g(x) = 4|x| − 3 maps a
person’s path from their house to
school, and their path from school
to a friend’s house. At what point
is the school located?

F (x)=x+3x find f(2)

f(x)=3x-2 find f(-10)

help please

While Vivian was visiting her sister in Springfield, she bought a set of bunk beds that was marked down 25% from an original price of $80. If the sales tax in Springfield is 10%, what was the total cost of the set of bunk beds?

A softball has a radius of 3 inches. What is the volume of the softball? Round your answer to the nearest whole number.

An FBI agent orders a block of ballistics gel. The gel weighs 54 pounds per cubic foot. What is the weight of the block of gel?

Triangle PQR will be rotated 90° counterclockwise about the origin.
What will be the coordinates of R'?

A.
(6, 3)

B.
(3, 6)

C.
(−3, −6)

D.
(1, 2)

Sam buys 3 different types of fruit in 3-fourths pound baskets. Maria has 1 and 1-fourth pounds fruit.



How many pounds of fruit do they have altogether?

What is the value of the constant in the equation that relates the height and
width of this rectangle?

The symbol used to seperate the tenths and ones is called a?

Cassie has a total of 110 coins in her piggy bank. All the coins are quarters and dimes. The coins have a total value of $20.30. How many quarters and how many dimes are in the piggy bank?

what is - 1/4 + 6 pls i need help

Find the 53rd term of the arithmetic sequence -12,-1,10

The cost of 7 chairs is equal to the cost of 2 tables. If the cost of 6 chairs and 5 tables is Rs.10,575, find the cost of 12 chairs.​

Suppose that a balanced, six-sided die has been altered so that the faces are 1, 2, 3, 4, 5, and 5. If the die is tossed five times, and the number on the uppermost face is recorded each time, what is the probability that the numbers recorded are 1, 2, 3, 4, and 5 in any order

PLASE ANSWER THISSSSSSS WILL GIVE BRAINLIST TO WRITE ANSWER

Find the measure of angel 1.

1. Sprint PCS offers a monthly cellular phone plan for $39.99. It includes 450 anytime minutes and charges $.45 per minute for additional minutes. a. x represents __________________ (2 points) b. f(x) represents ___________________ (2 points) c. Write out your piecewise function, including the domain.

Help Please! I'll Give Brainliest!

Roshanda was curious if students in her class would complete a maze faster if fast-paced music was playing in the background. She randomly assigned each student in her class to one of three groups: fast-paced music, slow-paced music, or no music. She timed each student as they individually completed a maze with their corresponding music (or no music) in the background. Students who worked with the fast-paced music, on average, completed the maze significantly faster than students in the other groups.
Can we conclude that the fast-paced music caused her classmates to finish the maze faster? Why?

(A) Yes, because the study included each student in her class

(B) Yes, because the adults were randomly selected

(C) Yes, because the students were randomly assigned to treatment and control groups

(D) Not necessarily, because the sample size was too small

(E) Not necessarily, because this wasn't an experiment

The sum of the angle measures of a quadrilateral is 360°. Write and solve an equation to find the value of x.
84° 68° 95° x°

2. The value, v, of the hat is less than $9.
what is the inequality ​

What transformation is described by the
notation (x, y) —> x,-y)?

A : translation left 1 unit
B : translation down 1 unit
C : reflection across the x-axis
D : reflection across the y-axis

HELPPPPPPP MEEEEEEEEEEEE

Please help me answer this:)

Will give you brainlst ^

I have 15 pounds of flour. How many batches of pizza dough can I make from 1 bag of flour?

y=1+sinx/cosx find dy/dx​

Simplify the expression:
- 3+ 40 - 80 ->