# Confidence iinterval problems

1. A researcher wishes to estimate with 99% Confidence, the proportion of adults who have high-speed internet access. Her estimate must be accurate within 5% of the true Proportion.

(a) Find the minimum sample needed, using a prior study that found that 54% of the respondents said they have high-speed internet access.

(b) No preliminary estimate is available. Find the minimum sample size needed.

n= ________. (Round up to the nearest whole number as needed.)

What is the minimum sample size needed assuming that no preliminary estimate is available.

n= _________ (Round up to the nearest whole number as needed).

2. You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and 95% Confidence Intervals for the Population Mean. Which interval is wider?

If convenient, use technology to construct the confidence intervals.

A random sample of 45 light-ounce serving of different juice drinks has a mean of 81.9 calories and a standard deviation of 44.8 calories.

The 90% Confidence interval is (_______, ____) Round to one decimal place as needed.)

The 95% confidence interval is (_______, ________). Round to one decimal place as needed.

Which interval is wider?

A. The 955 Confidence Interval

B. The 90% Confidence Interval

3. Use the Confidence Interval to find the Margin of Error and the Sample Mean

(0.084, 0.260)

The Margin of Error is _________.

The Sample Mean is ___________

4. You randomly Select and Measure the Contents of 10 bottles of cough syrup. The results (in fluid ounces) are shown below:

4.219 4.291 4.259 4.241 4.185

4.243 4.264 4.249 4. 221 4.237

Assume the Sample is taken from a normally distributed population; Construct99% Confidence intervals for (a) the population variance and (b) the population Standard Deviation.

(a) The confidence interval for the population Variance is (________, _______.) Round to six decimal places as needed.

(b) The confidence interval for the population standard Deviation is (_______, ______). Round to four decimal places as needed.

5. An election pool that a candidate had an approval rating of 41% with a margin of Error, E of 31%. Construct a confidence interval for the population of adults who approve the candidate.

The confidence interval for the population of adults who approve the candidate is (______, ______). Round to two decimal places.

6. Find the minimum sample size n, needed to estimate u for the given values of C, and E.

C=0.90, s=5.7, and E=1

Assume that a preliminary sample has at least 30 members

N=________. Round to the nearest whole number.

The state test scores of 12 randomly selected high school seniors are show below:

1430 1227 984

695 723 839

727 750 549

627 1442 947

Assume the population is normally distributed.

(a) Find the Mean

M= ________ (Round to one decimal place as needed).

(b) Find the sample standard deviation.

S=________ (Round to one decimal place as needed).

(c) Construct a 99% Confidence Interval for the population mean.

A 99% Confidence interval for the population mean is (________, _______). Round to one decimal place as needed.

P.S: please round up as instructed.

#### Solution Summary

Step by step method for computing test statistic for constructing confidence intervals