Mathematics, 11.02.2021 23:10 kami2006

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 the90% 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% confidenceinterval, 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.

Answers: 3

Show answers

Answers

Answer from: ponyolovezsosuk8683

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% confidenceinterval, and 95% confident for the 95% interval.

Step-by-step explanation:

90% confidence interval:

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

$\alpha = \frac{1 - 0.9}{2} = 0.05$

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

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

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.645\frac{11.36}{\sqrt{40}} = 2.95$

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 $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

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

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

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.96\frac{11.36}{\sqrt{40}} = 3.52$

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% confidenceinterval, and 95% confident for the 95% interval.

Answer from: Quest

mr. graef told us it is 13 pints

step-by-step explanation:

Answer from: Quest

i think 1: 2

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 16:20

Find the value of x for which abcd must be a parallelogram -9-6x x-30

Answers: 2

Answer

Mathematics, 21.06.2019 17:10

Determine whether the points (–3,–6) and (2,–8) are in the solution set of the system of inequalities below. x ? –3 y < 5? 3x + 2 a. the point (–3,–6) is not in the solution set, and the point (2,–8) is in the solution set. b. neither of the points is in the solution set. c. the point (–3,–6) is in the solution set, and the point (2,–8) is not in the solution set. d. both points are in the solution set.

Answers: 3

Answer

Mathematics, 21.06.2019 20:30

Arectangle has a width of 5 cm and a length of 10 cm. if the width is increased by 3, how does the perimeter change?

Answers: 1

Answer

Mathematics, 21.06.2019 21:00

From the beginning of the day the temperature rose 15 degrees so that by 4 pm it was 87 degrees. what was the temperature at the start of the day

Answers: 1

Answer

You know the right answer?

You are given the sample mean and the population standard deviation. Use this information to constru...