# Confidence Interval, Margin of Error & Sample Size

1. Use the confidence interval to find the estimated margin of error. Then find the sample mean.

A biologist reports a confidence interval of (1.5, 2.9) when estimating the mean height (in centimeters) of a sample of seedlings.

The estimated margin of error is _________.

The sample mean is _________.

2. You work for a consumer advocate agency and want to find the mean repair cost of a washing machine. As part of your study, you randomly select 35 repair costs and find the mean to be $116.00. The sample standard deviation is $17.30.

(a) Construct a 95% confidence interval for the population mean repair cost.

The 95% confidence interval for the population mean repair cost.

The 95% confidence interval is __________. (Round to two decimal places as needed.)

3. A machine cuts plastic into sheets that are 50 feet (600 inches) long. Assume that the population of lengths is normally distributed.

(a) The company wants to estimate the mean length the machine is cutting the plastic within 0.25 inch. Determine the sample size required to construct a 90% confidence interval for the population mean. Assume the population standard deviation is 0.50 inch.

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

4. The grade point averages (GPA) for 12 randomly selected college students are shown below.

2.2 3.5 2.7

1.8 0.6 4.0

2.2 1.5 3.6

0.2 2.2 3.5

(a) Find the sample mean.

x-bar = _____ (Round to two decimal places as needed.)

5. In a random sample of 38 bolts, the mean length was 1.26 inches and the standard deviation was 0.07 inch. Use a normal distribution or a t-distribution to construct a 99% confidence interval for the mean.

Which distribution should be used to construct the 99% confidence interval?

6. Let p be the population proportion for the following condition. Find the point estimates for p and q.

A study of 4698 adults from country A found that 2960 were obese or overweight.

The point estimate for p is ________ (Round to three decimal places as needed.)

7. The table below shows the results of a survey in which 400 adults from the East, 400 adults from the South, 400 adults from the Midwest, and 400 adults from the West were asked if traffic congestion is a serious problem.

Adults who say that traffic congestion is a serious problem

East 36%

South 33%

Midwest 25%

West 55%

(a) Construct a 99% confidence interval for the proportion of adults from the South who say traffic congestion is a serious problem.

8. A researcher wishes to estimate, with 90% confidence, the percentage of adults who support abolishing the penny. His estimate must be accurate within 3% of the true proportion.

(a) Find the minimum sample size needed using a prior study that found that 22% of the respondents said they support abolishing the penny.

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

9. Find the critical values X2L and X2R for the given confidence level c and sample size n.

c = 0.8, n = 28

X2L = ________ (Round to three decimal places as needed.)

10. You randomly select an measure the contents of 10 bottles of cough syrup. The results (in fluid ounces) are shown.

4.212 4.293 4.256 4.245 4.182

4.234 4.264 4.241 4.224 4.233

Assume the sample is taken from a normally distributed population. Construct 99% confidence intervals for (a) the population variance σ2 and (b) the population standard deviation σ.

(a) The confidence interval for the population variance is _______.

(Round to six decimal places as needed.)

(a) The confidence interval for the population standard deviation is _______.

(Round to four decimal places as needed.)

See attached file.

#### Solution Summary

The solution provides step by step method for the calculation of confidence interval, margin of error, sample size, sample mean and sample standard deviation. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.