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Question: A random sample of 80 observations results


A random sample of 80 observations results in 50 successes.
a. Construct the 95% confidence interval for the population proportion of successes.
b. Construct the 95% confidence interval for the population proportion of failures.


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> A random sample of 100 observations results in 40 successes. a. What is the point estimate for the population proportion of successes? b. Construct 90% and 99% confidence intervals for the population proportion. c. Can we conclude at 90% confidence that

> The manager of a newly opened Target store wants to estimate the average expenditure of his customers. From a preselected sample, the standard deviation was determined to be $18. The manager would like to construct the 95% confidence interval for the mea

> The manager of a pizza chain in Albuquerque, New Mexico, wants to determine the average size of their advertised 16-inch pizzas. She takes a random sample of 25 pizzas and records their mean and standard deviation as 16.10 inches and 1.8 inches, respecti

> An analyst would like to construct 95% confidence intervals for the mean stock returns in two industries. Industry A is a high-risk industry with a known population standard deviation of 20.6%, whereas Industry B is a low-risk industry with a known popul

> An analyst from an energy research institute in California wishes to estimate the 99% confidence interval for the average price of unleaded gasoline in the state. In particular, she does not want the sample mean to deviate from the population mean by mor

> Mortgage lenders often use FICO scores to check the credit worthiness of consumers applying for real estate loans. In general, FICO scores range from 300 to 850 with higher scores representing a better credit profile. A lender in a Midwestern town would

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> According to the Bureau of Labor Statistics, it takes an average of 22 weeks for someone over 55 to find a new job, compared with 16 weeks for younger workers (The Wall Street Journal, September 2, 2008). Assume that the probability distributions are nor

> Suppose that the miles-per-gallon (mpg) rating of passenger cars is a normally distributed random variable with a mean and a standard deviation of 33.8 mpg and 3.5 mpg, respectively. a. What is the probability that a randomly selected passenger car gets

> A professional basketball team averages 80 points per game with a standard deviation of 10 points. Assume points per game follow the normal distribution. a. What is the probability that a game’s score is between 60 and 100 points? b. What is the probabil

> You need to compute the 99% confidence interval for the population mean. How large a sample should you draw to ensure that the sample mean does not deviate from the population mean by more than 1.2? (Use 6.0 as an estimate of the population standard devi

> A sample of 80 results in 30 successes. a. Calculate the point estimate for the population proportion of successes. b. Construct 90% and 99% confidence intervals for the population proportion. c. Can we conclude at 90% confidence that the population prop

> Find the required sample size for estimating the population mean in order to be 95% confident that the sample mean is within 10 units of the population mean. Assume that the population standard deviation is 40.

> At a local community college, 40% of students who enter the college as freshmen go on to graduate. Ten freshmen are randomly selected. a. What is the probability that none of them graduates from the local community college? b. What is the probability tha

> The time required to assemble an electronic component is normally distributed with a mean and a standard deviation of 16 minutes and 4 minutes, respectively. a. Find the probability that a randomly picked assembly takes between 10 and 20 minutes. b. It i

> Let X represent a binomial random variable with n = 200 and p = 0.77. Find the following probabilities. a. P (X ≤ 150) b. P (X > 160) c. P (155 ≤ X ≤ 165) d. P (X = 160)

> A survey conducted by CBS News asked 1,026 respondents: “What would you do with an unexpected tax refund?” The responses are summarized in the following table. Response ………………………………………………………………………………... Frequency Pay off debts ……………………………………………………………………

> An accounting professor is notorious for being stingy in giving out good letter grades. In a large section of 140 students in the fall semester, she gave out only 5% A’s, 23% B’s, 42% C’s, and 30% D’s and F’s. Assuming that this was a representative clas

> Let X represent a binomial random variable with n = 150 and p = 0.36. Find the following probabilities. a. P (X ≤ 50) b. P (X = 40) c. P (X > 60) d. P (X ≥ 55)

> In a recent poll of 760 homeowners in the United States, one in five homeowners reports having a home equity loan that he or she is currently paying off. Using a confidence coefficient of 0.90, derive the interval estimate for the proportion of all homeo

> In an NBC News/Wall Street Journal poll of 1,000 American adults conducted August 5–9, 2010, 44% of respondents approved of the job that Barack Obama was doing in handling the economy. a. Compute the 90% confidence interval for the proportion of American

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> Assume in a sample of size n = 50. a. Construct the 95% confidence interval for the population proportion. b. What happens to the margin of error if the above sample proportion is based on n = 200 instead of n = 50?

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> The weight of turkeys is normally distributed with a mean of 22 pounds and a standard deviation of 5 pounds. a. Find the probability that a randomly selected turkey weighs between 20 and 26 pounds. b. Find the probability that a randomly selected turkey

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> Let X be normally distributed with mean μ = 10 and standard deviation σ = 4. a. Find P (X ≤ 0). b. Find P (X > 2). c. Find P (4 ≤ X ≤ 10). d. Find P (6 ≤ X ≤ 14).

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> As reported by tradingeconomics.com on September 2, 2012, the unemployment rates (in %) in major economies around the world were as follows: Country ……………………………………………………………………... Unemployment Rate Australia ……………………………………………………………………....................

> Let X be normally distributed with mean μ = 10 and standard deviation σ = 6. a. Find P (X ≤ 0). b. Find P (X > 2). c. Find P (4 ≤ X ≤ 10). d. Find P (6 ≤ X ≤ 14).

> The effort to reward city students for passing Advanced Placement tests is part of a growing trend nationally and internationally. Financial incentives are offered in order to lift attendance and achievement rates. One such program in Dallas, Texas, offe

> Let X be normally distributed with mean μ = 2.5 and standard deviation σ = 2. a. Find P (X > 7.6). b. Find P (7.4 ≤ X ≤ 10.6). c. Find x such that P (X > x) = 0.025. d. Find x such that P (x ≤ X ≤ 2.5) = 0.4943.

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> Mark Underwood is a professor of economics at Indiana University. He has been teaching Principles of Economics for over 25 years. Professor Underwood uses the following scale for grading. Grade ………………………………………………………………………………… Probability A …………………………………

> Organizers of an outdoor summer concert in Toronto are concerned about the weather conditions on the day of the concert. They will make a profit of $25,000 on a clear day and $10,000 on a cloudy day. They will take a loss of $5,000 if it rains. The weath

> A random sample of eight drugstores shows the following prices (in $) of a popular pain reliever: Assume the normal distribution for the underlying population to construct the 90% confidence interval for the population mean. 3.50 4.00 2.00 3.00 2.5

> Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 22, 18, 14, 25, 17, 28, 15, 21. a. Calculate the sample mean and the sample standard deviation. b. Construct the 80% confidence interva

> An analyst has developed the following probability distribution for the rate of return for a common stock. a. Calculate the expected rate of return. b. Calculate the variance and the standard deviation of this probability distribution. Scenario Pro

> You were informed at the nursery that your peach tree will definitely bloom sometime between March 18 and March 30. Assume that the bloom times follow a continuous uniform distribution between these specified dates. a. What is the probability that the tr

> The Netherlands is one of the world leaders in the production and sale of tulips. Suppose the heights of the tulips in the greenhouse of Rotterdam’s Fantastic Flora follow a continuous uniform distribution with a lower bound of 7 inches and an upper boun

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> Find tα, df from the following information. a. α = 0.025 and df = 12 b. α = 0.10 and df = 12 c. α = 0.025 and df = 25 d. α = 0.10 and df = 25

> A safety officer is concerned about speeds on a certain section of the New Jersey Turnpike. He records the speeds of 40 cars on a Saturday afternoon. The accompanying table shows a portion of the results. Assume that the population standard deviation is

> An economist wants to estimate the mean hourly wage (in $) of all workers. She collects data on 50 hourly wage earners. A portion of the data is shown in the accompanying table. Assume that the population standard deviation is $6. Construct and interpret

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> Suppose the 95% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$36,080, $43,920]. The population standard deviation used for the analysis is known to be $12,000. a. What is the point estimate of the me

> U.S. consumers are increasingly viewing debit cards as a convenient substitute for cash and checks. The average amount spent annually on a debit card is $7,790 (Kiplinger’s, August 2007). Assume that this average was based on a sample of 100 consumers an

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> A random variable X follows the continuous uniform distribution with a lower limit of 750 and an upper limit of 800. a. Calculate the mean and the standard deviation for the distribution. b. What is the probability that X is less than 770?

> A random variable X follows the continuous uniform distribution with a lower limit of 10 and an upper limit of 30. a. Calculate the mean and the standard deviation for the distribution. b. What is the probability that X is greater than 22? c. What is the

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> Find Zα⁄2 for each of the following confidence levels used in estimating the population mean. a. 90% b. 98% c. 88%

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> Consider the following hypothesis test: A random sample of 36 observations yields a sample mean of &acirc;&#136;&#146;125. The population standard deviation is 42. Conduct the test at &Icirc;&plusmn; = 0.01. H μ=-100 H: μ+-100 –100

> Consider the following hypothesis test: A random sample of 100 observations yields a sample mean of 80. The population standard deviation is 30. Calculate the p-value. What is the conclusion to the test if &Icirc;&plusmn; = 0.10? μ< 75 μ> 75 Hoi fe

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> Consider the following hypotheses: A sample of 16 observations yields a sample mean of 95. Assume that the sample is drawn from a normal population with a population standard deviation of 10. a. Calculate the value of the test statistic. b. Find the p-

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