Question

A.Express the confidence interval 631<μ<714.2631<μ<714.2 in the form of ¯x±MEx¯±ME.

¯x±ME=_____±______

B.You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=38.8σ=38.8. You would like to be 99.5% confident that your esimate is within 4 of the true population mean. How large of a sample size is required?
n =
Do not round mid-calculation. However, use a critical value accurate to three decimal places — this is important for the system to be able to give hints for incorrect answers.

C.Waitresses and waiters at a restaurant are trying to estimate the average tip on a given day. At StatKey, select CI for Single Mean, Median, St.Dev., then change the data set to Resturant Tips (Tip).

Create a sampling distribution by running at least 6000 samples based on their data set. Find a 95% confidence interval for the average daily tip at this resturant.

Mean	±±	EBM
	±±

D.In a survey, 19 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $32 and standard deviation of $2. Find the margin of error at a 99% confidence level.

Give your answer to two decimal places

Answer 1

A.

The given confidence interval for a population mean is,

That is, lower bound of confidence interval = 631 and

Upper bound of confidence interval = 714.2

The point estimate (xbar) and margin of error (ME)

The formula to find the point estimate is,

and the formula to find the margin of error is,

The given interval in the form of is

B.

Given: , the margin of error (ME) = 4 and c = confidence level = 99.5% = 0.995

The formula to find the sample size is,

Where Z - is the critical value at a given confidence level

To find the Z critical value the area 1 = (alpha/2) that is area to the left of Z is needed

alpha = 1 - c = 1 - 0.995 = 0.005

alpha/2 = 0.0025, 1 - (alpha/2) = 1 - 0.0025 = 0.9975

The z critical value uisng technology like excel for the area 0.9975 is 2.807

Type the function in one empty cell as =normsinv(0.9975) and enter to get 2.807

The sample size is,

Rounded to the next whole number is 742.

The sample of size 742 is required.

C. Data needed to simulate the sample and also for finding the confidence interval.

D.

Given: n = number of surveyed people = 19

Mean = 32, standard deviation = 2 and c = confidence level = 99% = 0.99

The formula to find the margin of error is,

Z - is the critical value at given confidence level

To find it the area 1 - (alpha/2) is needed.

alpha = 1 - 0.99 = 0.01

alpha/2 = 0.005 => 1 - (alpha/2) = 1 - 0.005 = 0.995

The z critical value for area 0.995 using excel is 2.576

The margin of error is,

Margin of error for 99% is 1.18