# General Statistics and Confidence Intervals

1. In the week before and the week after a holiday, there were 10.000 total deaths, and 4976 of them occurred in the week before the holiday.

A. Construct a 95% confidence interval to estimate of the proportion of deaths in the week before the holiday to the total deaths in the week before and the week after the holiday.

B. Based on the result, does there appear to be any indication that people can temporarily postpone their deaths to survive the holiday?

a. __________ < P < _________ (Round to three decimal places as needed)

b. Based on the result, does their appear to be any indication that people can temporarily postpone their death to survive the holiday.

Yes, because the proportion could not easily equal 0.5. The interval is substantially less than 0.5 the week before the holiday.

No, because the proportion could easily 0.5. The interval is not less than 0.5 the week before the holiday.

ó

2. Calculate the margin of error E = z a/2 * √ if the necessary requirements are satisfied.

The confidence level is 99%, the sample size is n-29, ó=19, and the original population is normally distributed.

Are the necessary requirements satisfied. Yes or No

E=____ (Round to three decimal places as needed).

3. Find the critical value z a/z that corresponds to the given confidence level

90%

Z a/z = _____ (Round to two decimal places as needed)

4. An IQ test is designed so that the mean is 100 and the standard deviation is 14 the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 99% confidence that the sample mean is with 3 IQ points of the true mean. Assume that ó =14 and determine the required sample size.

n = ____ (Round up to the nearest integer)

5. Randomly selected students participated in an experiment to test their ability to determine when one minute (or sixty seconds) has passed. Forty students yielded a sample mean of 60.9 seconds. Assuming that ó = 8.7 seconds, construct and interpret a 99% confidence interval estimate of the population mean of all students.

What is the 99% confidence interval for the population mean µ?

_______ < µ<_______

(Type an integer or decimal rounded to one decimal place as needed)

Based on the result, is it likely the students estimate have a mean that is reasonably close to sixty seconds?

A. Yes, because the confidence interval includes sixty seconds.

B. Yes, because the confidence interval does not include sixty seconds.

C. No, because the confidence interval does not include sixty seconds.

D. No, because the confidence interval includes sixty seconds.

6. Use the given confidence level and sample data to find:

A. The margin of error.

B. the confidence interval for the population mean µ. Assume the population has a normal distribution

Weight lost on a diet 90% confidence. N=41, x=2.0 kg s= 3.1 kg

a. E = ______ kg (round to one decimal place as needed)

b. What is the confidence interval for the population mean µ

_____ kg < µ < ______ kg (Round to one decimal place as needed)

7. Use the given data to find the minimum sample size required to estimate a population proportion or percentage.

Margin of error; 0.08; confidence level 90% p and q unknown

n=____(Round up to the nearest interger)

8. Do one of the following, as appropriate.

a. Find the critical value z a/z

b. Find the critical value t µ/z

State that neither normal nor the t distribution applies.

Confidence level 99% n= 27, ó us unknown population appears to be normally distributed.

Find the critical value

t a/z = 2.779

z a/z = 2.33

z a/z =2.58

t a/z = 2.479

Neither normal not t distribution applies

9. Use the given confidence interval limits to find the point estimate P and the margin of error E.

( 0.691, 0.855)

P^ =_______

E= ________

10. Assume that a random sample is used to estimate a population proportion P find the margin of error E that corresponds to the given statistics and confidence.

N =550, x = 330, 90% confidence

The margin of error E = _____

(Round to four decimal places as needed)