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# Confidence Interval

### 4 Statistics problems: Confidence interval estimate of mean

Q-3a. A stationery store wants to estimate the mean retail value of greeting cards purchased by its customers when they visit the store. A random sample of 15 customers indicates a mean amount of \$2.55 with a standard deviation of \$0.44 per customer per visit. Assuming a normal distribution, construct a 95% confidence inter

### Confidence Interval for Population Proportion Survey

A survey of 705 workers asked how much they used the Internet at work. 423 said they used it within limits, and 183 said that they did not use the Internet at work. Construct a 95% confidence interval estimate for the proportion of all workers who use the Internet within limits.

### Statistics: Confidence interval estimate for mean paper length

A paper manufacturer has a production process that operates continuously throughout an entire production shift. The paper is expected to have a mean length of 11 inches, and the standard deviation of the length is 0.02 inches. At periodic intervals, a sample is selected to determine whether the mean paper length is still equal

### Using MegaStat for confidence intervals

According to a national survey of 1,800 Traditional Bank customers, 1,200 of them were either satisfied or very satisfied with customer service. Find a 95% confidence interval for the true proportion of customers who are either satisfied or very satisfied with customer service. Use MegaStat for your computations. Round y

### Confidence intervals: swine flu example

According to an early CDC study of 21 patients infected with the swine flu, the average incubation period was 7 days with a sample standard deviation of 4.5 days. We will assume that the incubation times are normally distributed. Find a 95% confidence interval for the true average incubation period. Use MegaStat for your co

### Confidence Interval - statistics

A survey of individuals who passed the BAR finds the average starting salary for lawyers to be \$75,215 for 36 individuals sampled. If the population standard deviation is \$15,990 find a 90% confidence interval for the true mean. Round your answers to the nearest whole number.

### Confidence Interval for Proportion

According to a national survey of 1,500 Silverman Sachs customers, 1,050 of them were either satisfied or very satisfied with their financial advisor. Find a 95% confidence interval for the true proportion of customers who are either satisfied or very satisfied with their financial advisor.

### Confidence Interval and Sample Size

Suppose we want to conduct a poll to estimate the proportion of voters who favor the new healthcare bill, and we plan to use a 95% confidence interval for our estimate. Determine the sample size needed so that the sample proportion is within a margin of error of 0.03 of the true proportion of all voters who are in favor of the b

### Determine Sample Size for a Confidence Interval: Braking distance of a Yamashita

Until this year the mean braking distance of a Yamashita motorcycle moving at 60 miles per hour was 160 feet. Yamashita engineers have developed what they consider a better braking system. They test the new braking system on a random sample of 20 motorcycles and determine the sample mean to be 145 feet, with a sample standard

### Probing the Pollsters

When pollsters report results of a poll, they often include the margin of error but not much more. If candidate X has 54 percent support of the voters with a margin of error of 3 percent, that means the candidate is predicted to have between 51 percent and 57 percent support in the election. Before jumping to conclusions

### In New York State, savings banks are permitted to sell a form of life insurance

See attached file. In New York State, savings bank are permitted to sell a form of life insurance called savings bank life insurance (SBLI). The approval process consists of underwriting, which includes a review of the application, medical information bureau check, possible request for additional medical information and medic

### Market researcher for consumer electronics company studies television viewing habits

A market researcher for a consumer electronics company wants to study the television viewing habits of residents of a particular area. A random sample of 40 respondents is selected and each respondent is instructed to keep a detailed record of all television viewing in a particular week. The results are as follows:

### In New York State, savings bank can sell a form of life insurance

In New York State, savings bank are permitted to sell a form of life insurance called savings bank life insurance (SBLI). The approval process consists of underwriting, which includes a review of the application, medical information bureau check, possible request for additional medical information and medical exams, and a policy

### Finding the Confidence Interval & Population Standard Deviation

A random sample of 16 students showed that the variance in the number of hours they spend studying for a final exam was 25 hours^2. a. Construct a 95% confidence interval for the population variance and standard deviation of hours spent studying. Assume the population of hours spent studying is normally distributed. b. Tes

### Hypothesis testing: wealth

Is there any difference between the proportion of Americans who wish they were rich and the proportion of Canadians who wish they were rich? A random sample of 1000 Americans showed that 550 wish they were rich, while a random sample of 500 Canadians showed that 225 wished they were rich. a. Find a 97.5% confidence interval f

### Statistics: Comparison of reaction times of 10 year olds, play video games and not

A researcher is comparing the reaction times of a 10-year-olds who play video games and 10-year-olds who do not. Random samples from each group provided the following results below: Reaction time of 10-year-olds

### Confidence interval: alpha grading system

I need some guidance for the following question: A survey was conducted to determine the percentage of students at a post-secondary institution who prefer the new alpha-grading system. The responses from a random sample of 30 students are shown below. Yes No Yes Yes No Yes No Yes Yes No Yes No Yes No Yes No Yes Yes Yes Ye

### Confidence Interval for Mean: mpg 2009 sedans

Using the below data for 2009 mpg of sedans priced under \$20,000: 27, 31, 30, 28, 27, 24, 29, 32, 32, 27, 26, 26, 25, 26, 25, 24 a. Construct a 95% confidence interval estimate for the population mean mpg of 2009 sedans priced under \$20000 assuming a normal distribution. b. Interpret the interval constructed in a.

### Statistics Problems

1. Given a normal distribution with mean,m =100 and standard deviation, s = 10, if you select a sample of n=25, what is the probability that x is a. less than 95? b. between 95 and 97.5? c. above 102.2? d. There is a 65% chance that X is above what value? 2. Time spent using e-mail per session is normally distri

### Exact Confidence Interval for Poisson Distribution

A temporary job is advertised annually. The number of applicants for the job is a random variable which is known from many years' experience to have a distribution Po(12). In 2010 there were 19 applicants for the job. Test, at the 10% significance level, whether there is evidence of an increase in the number of applicant for the

### Reasoning for conclusion about mean operating cost for the fleet of delivery trucks

A delivery truck manager takes a sample of 25 delivery trucks and calculates the sample mean and deviation for the cost of operation. A 95% confidence interval for the mean cost is constructed and found to be \$253 to \$320. He reasons that this interval contains the mean operating cost for the fleet of delivery trucks since the s

### Finding the confidence interval for poll or survey results

Quality Progress, Feburary 2005, reports on the results achieved by Bank of America in improving customer satisfaction and customer loyalty by listening to the "voice of the customer". A key measure of customer satisfaction is the response on a scale from 1 to 10 to the question: "Considering all the business you do with Bank of

### Confidence interval, how many executives should be interviewed

A survey is being planned to determine the mean amount of time corporate executives watch television. The pilot indicated the mean time is 12 hours with a standard deviation of 3 hours. It is desired to estimate the mean viewing time within one-quarter hour. Using the 95% confidence interval, how many executives should be int

### Formulate an 84% interval estimate for a true proportion

1) The Target Corporation personnel director wants to estimate the number of employees within one year of retirement. A random sample of 120 employee records is selected, and 36 people are found to be within one year of retirement. Formulate an 84% interval estimate for the true proportion of employees within one year of retir

### Statistics Problems: Mean, probability, standard deviation, confidence interval

1. You are a manager of a Starbucks located at Southcenter Mall. Recently, a new local coffee shop specializing in lattes has opened in the Mall. You are wondering what the impact on your latte sales may be. You know from previous data tracking that the largest number of lattes sold at your location is during the morning. T

### Determine: Maximum Error of Estimate and Confidence Level

A confidence interval estimate for the population mean is given to be (41.16, 49.85). If the standard deviation is 16.290 and the sample size is 54, answer each of the following (show all work): (A) Determine the maximum error of the estimate, E. (B) Determine the confidence level used for the given confidence interva

### Estimate the mean amount spent on birthday gifts for a typical family

A study was conducted to estimate the mean amount spent on birthday gifts for a typical family having two children. A sample of 195 was taken, and the mean amount spent was \$182.25. Assuming a standard deviation equal to \$42.16, find the 95% confidence interval for m, the mean for all such families (show all work).

### Measure time it takes a product component to move from one workstation to the next

By measuring the amount of time it takes a component of a product to move from one workstation to the next, an engineer has estimated that the standard deviation is 3.22 seconds. Answer each of the following (show all work): (A) How many measurements should be made in order to be 98% certain that the maximum error of esti

### Bank customer and bank manager

In the bank customer waiting time case, a bank manager had developed a new system to reduce the time customers spend waiting to be served by tellers during peak business hours. Typical waiting times during peak business hours under the current ystem are roughly 9 to 10 minutes The bank manager hopes that the new system will lo

### How to Solve for Confidence Intervals

Question: A sample of 119 golfers showed that their average score on a particular golf course was 93.54 with a standard deviation of 6.16. Answer each of the following (show all work and state the final answer to at least two decimal places): (A) Find the 98% confidence interval of the mean score for all 119 golfers. (B)