The 95 Percent Confidence Interval for The Population Mean Problem

I’m working on a statistics question and need an explanation and answer to help me learn.

1. Determine the 95% confidence interval estimate for the population mean of a normal distribution given n=100, σ=102, and x=1,200

The 95% confidence interval for the population mean is from

to

(Round to two decimal places as needed. Use ascending order.)

2. A random sample of n=12 values taken from a normally distributed population resulted in the sample values below. Use the sample information to construct a 99% confidence interval estimate for the population mean.

The 99% confidence interval is from

$

to

$

3. As a follow-up to a report on gas consumption, a consumer group conducted a study of SUV owners to estimate the mean mileage for their vehicles. A simple random sample of 80 SUV owners was selected, and the owners were asked to report their highway mileage. The results that were summarized from the sample data were x=19.5 mpg and s=5.4 mpg. Based on these sample data, compute and interpret a 99% confidence interval estimate for the mean highway mileage for SUVs.

The 99%

confidence interval is

mpg–mpg.

(Round to one decimal place as needed. Use ascending order.)

4. An advertising company wishes to estimate the mean household income for all single working professionals who own a foreign automobile. If the advertising company wants a 95% confidence interval estimate with a margin of error of ±2800,what sample size is needed if the population standard deviation is known to be $24,500?

The sample size must be at least enter your response here.

(Round up to the nearest whole number.)

5.An airline is considering charging a two-tiered rate for checked bags based on their weight. Before deciding at what weight to increase the rate, the airline wishes to estimate the mean weight per bag checked by passengers. It wants the estimate to be within ±0.50

pounds of the true population mean. A pilot sample of checked bags produced the results shown below.

a. The sample size must be at least enter your response here.

(Round up to the nearest whole number.)

6.A magazine company is planning to survey customers to determine the proportion who will renew their subscription for the coming year. The magazine wants to estimate the population proportion with 99%

confidence and a margin of error equal to

±0.08.

What sample size is required? critical values for commonly used confidence levels.

The required sample size is customers.

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

7. Suppose that a safety group surveyed 1,400 drivers. Among those surveyed, 73% said that careless or aggressive driving was the biggest threat on the road, and 34% said that cell phone usage by other drivers was the driving behavior that annoyed them the most. Based on these data and assuming that the sample was a simple random sample, construct and interpret a 95% confidence interval estimate for the true proportion in the population of all drivers who are annoyed by cell phone users.

The confidence interval estimate is –enter your response here.

(Round to three decimal places as needed. Use ascending order.)

8. A multinational corporation employing several thousand workers at its campus in a large city would like to estimate the proportion of its employees who commute to work by any means other than automobile. The company hopes to use the information to develop a proposal to encourage more employees to forgo their automobiles as a part of their commute. A pilot study of 100 randomly sampled employees found that 20 commute to work by means other than an automobile. Complete parts a and b below.

a. How many more employees must the company randomly sample to be able to estimate the true population of employees who commute to work by means other than an automobile with a margin of error of 0.02 and a level of confidence of 99%?

The company must sample more employees.