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# Confidence Interval

### Confidence

9.4 An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. If a sample of 30 bulbs has an average life of 780 hours, find a 96% confidence interval for the population mean of all bulbs produced by this firm. 9.6 The heights of a

### Constructing a Confidence Interval for Test Results

Thirty randomly selected students took the calculus final. If the sample mean was 78 and the standard deviation was 7.5, construct a 99 percent confidence interval for the mean score of all students.

### Confidence Intervals and Control Limits

The operation time is calculated for scenarios one and two. The point of the exercise is to identify the scenario that takes the least amount of time ie... the time difference between the two scenarios. Explain the control limits (see word .doc) and calculate them upper and lower limits. Calculate confidence intervals and exp

### Confidence Intervals for Population Proportion P

USE THE GIVEN DEGREE OF CONFIDENCE AND SAMPLE DATA TO CONSTRUCT A CONFIDENCE INTERVAL FOR THE POPULATION PROPORTION P N = 102 X= 52; 88 PERCENT ANSWERS .433 LESS THAN P LESS THAN .587 .428 LESS THAN P LESS THAN .592 .432 LESS THAN P LESS THAN .588 .429 LESS THAN P LESS THAN .591

### From the Data Set below select a sample of 20 values and find the 90% confidence interval of the mean of the number of the acres. Find the mean of all values, and determine if the confidence interval contains the mean.

Problem: From the Data Set below select a sample of 20 values and find the 90% confidence interval of the mean of the number of the acres. Find the mean of all values, and determine if the confidence interval contains the mean. DATA SET VI Acreage of U.S. National Parks, in Thousands of Acres 41 66 233 775 1

### Fashion Industries: Develop a 99% interval for portion of applicants that fail drug test

As a condition of employment, Fashion Industries applicants must pass a drug test. Of the last 220 applicants, 14 failed the test. Develop a 99 percent interval for the proportion of applicants that fail the test. Would it be reasonable to conclude that more than 10 percent of the applicants are now failing the test?

### Compute the 95% Confidence Interval

What information does a confidence interval give? A sample of 50 employees was taken and the average number of children in each of the employee's family was computed to be 2.1 with a standard deviation of 0.5. Compute the 95% confidence interval on the average number of children. Interpret the answer.

### Confidence interval

In an effort to estimate the mean amount spent per household per month in a small Canadian town, data were collected for a sample of 50 households. The sample showed an average amount of \$2000 and a standard deviation of \$500. a. Develop a 90% confidence interval estimate of the population mean amount spent. b. D

### Sampling Variability and Standard Error

Based on a simple random sample of one hundred an analyst estimates the average hourly wage earned by workers in a city to be \$30 and computes the margin of error to be \$5. Can we conclude from this that most workers there earn between \$25 and \$35 per hour? Is this the right interpretation for the margin of error?

### Calculations with confidence intervals

Pollsters try to determine whether or not a person is a "likely voter" before they count their opinion in a poll. If we assume 40% of the registered voters will actually vote, in a random sample of 100 registered voters we can be 95% confident that somewhere between ___ and____ of them will actually vote. Fill in the blanks with

### (a)What statement can you make about the range \$300 to \$700? (b)What statement can you make about the range \$480 to \$520?

A large population of overdue bills has balances that follow a normal curve. When we take a sample of 100 of these these average is \$500 and the SD is \$100. (a)What statement can you make about the range \$300 to \$700? (b)What statement can you make about the range \$480 to \$520?

### Variance of Repair Cost for Dishwashers

1.) The following data set represents the repair cost (in dollars) for a random sample of 30 dishwashers (adapted from Consumer Reports) 41.82 90.07 100.05 118.77 52.81 90.35 101.32 119.01 57.80 91.68 103.59 120.70 68.16 91.72 104.19 140.52 73.48 93.01 105.62 141.84 78.88 95.21 111.32 147.06 88.13

### Construction of Confidence Intervals

A sample of 100 cans of coffee showed an average weight of 13 ounces. The population standard deviation is 0.8 ounces. a. Construct a 95% confidence interval for the mean of the population. b. Construct a 95.44% confidence interval for the mean of the population. c. Discuss why the answers in parts a and b are differe

### Developing a 95 Percent Confidence Interval

In a random sample of 150 residents of New Hampshire, 90 residents indicated that they voted for the Republican candidate in the last presidential election. Develop a 95% confidence interval for the proportion of all New Hampshire residents who voted for the Republican candidate.

### Calculating the 99 Percent Confidence Interval

A sample of 16 patients in a doctor's office showed that they had to wait an average of 43 minutes with a standard deviation of 8 minutes before they could see the doctor. Provide a 99% confidence interval for the average waiting time of all the patients who visit this doctor.

### Number of Days Company should Sample given Margin Error

A coal company wants to determine a 95% confidence interval estimate for the average daily tonnage of coal which they mine. Assuming that the company reports that the standard deviation of daily output is 80 tons, how many days should they sample so that the margin of error is 20 tons.

### Confidence Interval for Mean....

Average electric usage was studied. A previously known population standard deviation was 450 KWH. A sample of 81 houses was studied and found to have a mean of 1858 KWH. Find the 95% confidence interval for the true mean.

### Confidence interval for population mean problem

Ford Motor Company wishes to estimate the mean dollar amount of damage done to a 1995 Taurus as result of a 10 mph crash into the rear bumper of a parked car. 36 Tauruses are test crashed into parked cars and the dollar amount of damage done to each is recorded. The results are x-bar = \$438 and s=\$86. a. Compute the 90% confi

### Calculation of Confidence Interval for Population Proportion

A random sample of 600 registered voters yields 360 in favor of the slow growth initiative. a. Compute the 99% confidence interval for the percentage of registered voters who favor the slow growth initiative. Interpret this interval. b. How many registered voters should be sampled in order to be 99% confident of being with

### Width of the confidence interval

Discuss what happens to the width of the confidence interval as the sample size is decreased. Discuss what happens to the width of the confidence interval as the confidence level is increased. Is this reasonable? Explain.

### Confidence Interval and Sample Size Determination

Families USA, a monthly magazine that discusses issues related to health and health costs, surveyed 20 of its subscribers. It found that the annual health insurance premiums for a family with coverage through an employer averaged \$10,979. The standard deviation of the sample was \$1,000. a. Based on this sample information, deve

### Statistics

Biting an unpopped kernel of popcorn hurts! As an experiment, a self-confessed biting an unpopped kernel of popcorn hurts! As an experiment, a self-confessed connoisseur of cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, the unpopped kernels were counted. There were 86. (a) Construct a 90 per

### Forecasting

Forecasting is not to clear to me, how do I get started? Given the following data on hotel check-ins for a 6-month period: Month Number of rooms July 70 August 105 September 90 October 120 November 110 December 115 a. What is the 3-month moving average for January? b. What is the 5-month moving average for Jan

### A) Determine the 95% confidence interval estimates of the mean medical costs for each of the four age categories. b) For each year listed, determine the 95% confidence interval estimates of the total medical costs for Canadians 45 years old and older.

12.3-question 1 A statistics practitioner has been given the task of making these predictions. Accordingly, random samples of four groups of Canadians were drawn. They are Group Ages 1 45-64 2 65-74 3 75-84 4 85 and over Age group 2011 2016 2021 2026 2031 45-64 9718 10013

### Statistics - Confidence Interval .

Describe the confidence interval for the survey of 10,000 families who are potential home buyers for homes in the following price ranges: \$130,000 - \$200,000, \$200,000 0 \$250,000 and \$250,000 - \$350,000. This is a research to assist financial institutions and realtors find potential home buyers.

### The Confidence Interval for the Population Mean

A random sample of 121 automobiles traveling on an interstate showed an average speed of 65 mph. From past information, it is known that the standard deviation of the population is 22 mph. Determine a 96.6% confidence interval for the mean.

### Determining Margin of Error: Example Problem

A Gallup Poll of 1002 adults found that 25% of the respondents said that their household had experienced a crime in the past year. Among respondents aged 18 to 29 years, 43% had been victims of a crime. Gallup says, "For results based on the total sample of national adults, one can say with 95% confidence that the margin of samp

### Speculations about a study result

This question is asking for speculation about the possible results of a study if we change the size of the population. It all depends on unknowns such as how representative the 100 adults are of the population. In general, the larger the population the more sure we are that it is representative of the population. In a poll o

### 99 percent confidence interval

1. A sample set of weights in pounds are 1.01, .95, 1.03, 1.04, .97, .97, .99, 1.01 and 1.03. Assume the population of weights are normally distributed. Find a 99 percent confidence interval for the mean population weight. 2. Based on a random sample of 25 units of product X, the average weight is 102 lbs. and the sample

### Developing Percent Confidence Intervals

1. The success rate of a surgical procedure is 70 per 100 cases examined in a sample. Find a 90 percent confidence interval for the total number of successes per 1,000 cases. 2. Ten items of 100 are defective. Develop a 95 percent confidence interval for the population proportion of defectives. 3. Assuming a normal popul