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# Confidence Interval

### Probability, Test Statistics and Error

In a recent year, scores on a standardized test for high schools student with a 3.50 to 4.00 grade point average were normally distributed, with a mean of 37.9 and a standard deviation of 2.4. A student with a 3.50 to 4.00 grade point average who took the standardized test is randomly selected. Four Decimal Places for Questi

### The Quick Method

The Quick Method: The quick method uses "p-hat +/- (1/?n)" as a rough recipe for a 95% confidence interval for a population proportion. The margin of error from the quick method is a bit larger than needed. It differs most from the more accurate method when p-hat is close to 0 or 1. An SRS of 500 motorcycle registrations finds t

### Smoking in the U.S.: Confidence Intervals

Smoking in the United States: An August 2007 nationwide random survey of 1012 adults asked whether they had smoked cigarettes in the last week. Among the respondents, 243 said they had. We can act as if the sample were an SRS. a. Give a 95% confidence interval for the proportion of all American adults who smoked in the week pre

### Solving for Confidence Intervals

Question: A sample of 240 observations is selected from a normal population for which the population standard deviation is known to be 24.The sample mean is 20. (a) Determine the standard error of the mean. (Round your answer to 3 decimal places) (b) Determine the 90% confidence interval for the population mean. (Round your

### Confidence intervals for the population mean

The owner of Britten's Egg Farm wants to estimate the mean number of eggs laid per chicken. A sample of 18 chickens shows they laid an average of 25 eggs per month with a standard deviation of 7 eggs per month. (a-1) What is the value of the population mean? It is unknown. 25 7 (a-2) What is the best e

### Solving for Point Estimates and Confidence Intervals

Question: The Warren County Telephone Company claims in its annual report that "the typical customer spends \$70 per month on local and long-distance service." A sample of 12 subscribers revealed the following amounts spent last month. Amounts Spent Last Month: \$64 \$57 \$59 \$68 \$60 \$65 \$69 \$56 \$58 \$56 \$55

### Margin of Error Calculations

1. The width of a confidence interval is always twice what value? 2. Suppose = 29:47 and x = 26:54. What is the sampling error? 3. Let c = 0:99, s = 5:6, and n = 87. What is the margin of error, E? 4. Construct the confidence interval for the population mean, . c = 0:90, x = 58:62, s = 1:84, and n = 65. Use the confidenc

### Finding the Confidence Interval for a Proportion in an Election

Prior to a statewide senate election, three polls are conducted concerning a particular candidate's popularity. In the first poll, 750 of 1500 voters favor the candidate. In the second poll, 1285 of 2520 favor the candidate. In the third poll, 1795 of 3500 voters favor the candidate. Find 95% confidence intervals for the proport

### Finding Margin of Error and 95% Confidence Interval

Assume that the population means are to be estimated from the sample described below. Use the sample results to approximate the margin of error and 95% confidence interval Sample size= 1,060 Sample size= \$46,233 Sample standard deviation= \$21,000 a) The margin of error is \$______ (please round tot the nearest dollar as ne

### Statistics and Confidence Intervals Deviations

Work on an Excel spreadsheet with results linked to data using Excel functions and cell addresses. To derive the confidence intervals for the mean with known standard deviation, use the z table from Table E.2 or =normsinv. 1) The Harvard class of 2009 had a reunion attended by 36 members. It was determined that they had mar

### Probability Problem Set

Problem 3 a. A random sample of 25 was drawn from a normal distribution with a standard deviation of 5. The sample mean is 80. Determine the 95% confidence interval estimate of the population mean. b. Repeat part (a) with a sample size of 100. c. Repeat part (a) with a sample size of 400. d. Describe what happens to the conf

### Sample Distribution Scenario Questions

Sample Distribution Questions: 1. A researcher is interested in determining the average number of years employees of a company stay with the company. If past information shows a standard deviation of 7 months, what size sample should be taken so that at 95% confidence the margin of error will be 2 months or less? 2. In a sa

### 95% Confidence Interval for a Sample of 60 Students

A sample of 60 students from a large university is taken. The average age in the sample was 22 years with a standard deviation of 6 years. Construct a 95% confidence interval for the average age of the population.

### Constructing Confidence Intervals for a Sample Distribution

The average monthly electric bill of a random sample of 256 residents of a city is \$90 with a standard deviation of \$24. a. Construct a 90% confidence interval for the mean monthly electric bills of all residents. b. Construct a 95% confidence interval for the mean monthly electric bills of all residents.

### Two questions related to constructing confidence intervals.

A sample of 144 cans of coffee showed an average weight of 16 ounces. The standard deviation of the population is known to be 1.4 ounces. a. Construct a 68.26% confidence interval for the mean of the population. b. Construct a 97% confidence interval for the mean of the population.

### Interval Estimates

Volunteers were randomly selected for a blind taste test between two flavored waters, A and B, at two different locations in the mall. Of 64 volunteers at the first location, 41 preferred product A. Of 58 volunteers at the second location, 35 preferred product A. Using interval estimates, determine to 95% confidence if there is

### Determine a 99% confidence interval for the true proportion

A random sample of 135 dentists indicated that 84 recommended sugarless gum for their patients that chew gum. What is a 99% confidence interval for the true proportion of dentists in the population that would make such a recommendation?

### Calculating and interpreting margin of error

The margin of error for polling results is typically determined as the half-width of a 95% confidence interval. With respect to a particular ballot proposition, a random sample of 423 voters indicated 51% support and 49% oppose the measure. What is the margin of error? Interpret the result.

### The importance of confidence intervals

Why do we care about confidence intervals? In most situations, we can't ever know whether our confidence interval is "correct" or "incorrect." Why bother?

### Confidence Intervals (Limits) and Testing with known and unknown population standard deviation (large n and small n)

You are a quality analyst with John and Sons Company. Your company manufactures fax machines, copiers, and printers that use plain paper. The CEO of the company wants the machines to handle 99.5 percent of all the paper that is used in them without the paper getting jammed. The CEO asks you to determine the thickness of paper th

### Value sample and interval

I am having problems with these sample problems. Can you please help me? I have attached the following questions within an excel sheet for your usage in deriving the solutions. A 90 % confidence interval for a situation is developed and is given by the following 48 < µ < 64. a) Give the value of the sample mean that was us

### Statistics Review Questions.

Choose the best answer to the following questions. 1. (TCO 9) The hours of study and the final exam grades have this type of relationship: ? = 7.35(hours) + 34.62. Based on this linear regression equation, estimate the expected grade for a student spending 8 hours studying. Round your answer to two decimal places.

### Confidence interval containing the...

Which is the best and why? A confidence interval (CI) is a range of scores with specific boundaries that should contain the ______ mean. A. sample B. population C. standard error D. none of the above

### Statistics Problem: Adolescents and Friends of a Different Race

A subsample of the 2008 MTF survey suggests that black adolescents are more accepting of having friends of a different race than white adolescents. Of the 184 black adolescents who answered the question about race and friendship, 44% reported that having friends of a different race is "desirable." However, of the 867 white adole

### Statistics Problem Set: USGA Golf Ball Test

5.70 USGA golf ball test. The United States Golf Association USGA tests al new brands of golf balls to ensure that they meet USGA specifications. One test conducted is intended to measure the average distance traveled when the ball is hit by a machine call "Iron Byron" a name inspired by the swing of the famous golfer Byron Nels

### Statistics Problem Set: Scanning Errors at Wal-Mart

5.60 It costs you \$10 to draw a sample of siz n = 1 and measure the attribute of interest. You have a budget of \$1,500. a. Do you have sufficient funds to estimate the population mean for the attribute of interest with a 95% confidence interval 5 units in width? Assume sigma = 14. b. If you used a 90% confidence level, would

### Statistics Problem Set: Intervals

5.2. What is the confidence level of each of the following confidence intervals for the mean? (see attached). 5.20. The "Raid" test kitchen. According to scientists, the cockroach has had 300 million years to develop a resistance to destruction. In a study conducted by researchers for S.C. Johnson & Son, Inc. (manufacturers o

### Hypothesis Testing and Confidence Intervals with Minitab

Your manager has speculated the following: a. the average (mean) annual income was less than \$50,000, b. the true population proportion of customers who live in an urban area exceeds 40%, c. the average (mean) number of years lived in the current home is less than 13 years, d. the average (mean) credit balance

### Confidence Interval Estimate - Lifetime of Light Bulbs

A random sample of the lifetime of 49 UltraIllum light bulbs has a mean of 3,960 hours and a standard deviation of 200 hours. Construct a 95% confidence interval estimate of the mean lifetime for all UltraIllum light bulbs.

### Randomized Double-Blind Clinical Trials

In randomized, double-blind clinical trials of a new vaccine, subjects were randomly divided into two groups. Subjects in group 1 received the new vaccine while subjects in group 2 received a control vaccine. After the first dose, 104 of 707 subjects in the experimental group (group 1) experienced fever as a side effect. After t