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free/or 0.5$ |
| m146 | A survey investigated the public’s attitude toward the federal deficit. Each sampled citizen was classified as to whether he or she felt the government should reduce the deficit or increase the deficit, or if the individual had no opinion. The sample results of the study by gender are reported below.
At the .05 significance level, is it reasonable to conclude that gender is independent of a person’s position on thedeficit? |
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| m147 | A survey of 36 randomly selected “iPhone” owners showed that the purchase price has a mean of $416 with a sample standard deviation of $180.
a. Compute the standard error of the sample mean.
b. Compute the 95% confidence interval for the mean.
c. How large a sample is needed to estimate the population mean within $10? |
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| m148 | A survey of 545 college students asked: What is your favorite winter sport? And, what type of college do you attend? The results are summarized below:
Using these 545 students as the sample, a student from this study is randomly selected.
a. What is the probability of selecting a student whose favorite sport is skiing?
b. What is the probability of selecting a junior-college student?
c. If the student selected is a four-year-college student, what is the probability that the student prefers ice skating?
d. If the student selected prefers snowboarding, what is the probability that the student is in junior college?
e. If a graduate student is selected, what is the probability that the student prefers skiing or iceskating? |
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| m149 | A survey of the number of phone calls made by a sample of 16 Verizon subscribers last week revealed the following information. Develop a stem-and-leaf chart. How many calls did a typical subscriber make? What were the maximum and the minimum number of callsmade? |
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| m150 | A telemarketer makes six phone calls per hour and is able to make a sale on 30% of these contacts. During the next 2 hours, find:
a. The probability of making exactly four sales.
b. The probability of making no sales.
c. The probability of making exactly two sales.
d. The mean number of sales in the 2-hour period. |
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| m151 | A test is to be conducted involving the mean holding power of two glues designed for plastic. First, a small plastic hook was coated at one end with Epox glue and fastened to a sheet of plastic. After it dried, weight was added to the hook until it separated from the sheet of plastic. The weight was then recorded. This was repeated until 12 hooks were tested. The same procedure was followed for Holdtite glue, but only 10 hooks were used. The sample results, in pounds, were:
At the .01 significance level, is there a difference between the mean holding power of Epox and that of Holdtite?
(a) The null and the alternate hypotheses,
(b) The decision rule, and
(c) The decision regarding the null hypothesis,
(d) Then interpret theresult. |
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| m152 | A total of 1,000 residents in Minnesota were asked which season they preferred. One hundred liked winter best, 300 liked spring, 400 liked summer, and 200 liked fall. Develop a frequency table and a relative frequency table to summarize this information. |
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| m153 | A total of 5.9% of the prime-time viewing audience watched shows on ABC, 7.6% watched shows on CBS, 5.5% on Fox, 6.0% on NBC, 2.0% on Warner Brothers, and 2.2% on UPN. A total of 70.8% of the audience watched shows on other cable networks, such as CNN and ESPN. You can find the latest information on TV viewing from the following website: http://www.zap2it.com/tv/ratings/. Develop a pie chart or a bar chart to depict this information. Write a paragraph summarizing your findings. |
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| m154 | A tube of Listerine Tartar Control toothpaste contains 4.2 ounces. As people use the tooth paste, the amount remaining in any tube is random. Assume the amount of toothpaste remaining in the tube follows a uniform distribution. From this information, we can determine the following information about the amount remaining in a toothpaste tube without invading anyone’s privacy.
a. How much toothpaste would you expect to be remaining in the tube?
b. What is the standard deviation of the amount remaining in the tube?
c. What is the likelihood there is less than 3.0 ounces remaining in the tube?
d. What is the probability there is more than 1.5 ounces remaining in the tube? |
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| m155 | A uniform distribution is defined over the interval from 2 to 5.
a. What are the values for a and b?
b. What is the mean of this uniform distribution?
c. What is the standard deviation?
d. Show that the total area is 1.00.
e. Find the probability of a value more than 2.6.
f. Find the probability of a value between 2.9 and 3.7. |
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| m156 | A uniform distribution is defined over the interval from 6 to 10.
a. What are the values for a and b?
b. What is the mean of this uniform distribution?
c. What is the standard deviation?
d. Show that the total area is 1.00.
e. Find the probability of a value more than 7.
f. Find the probability of a value between 7 and 9. |
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| m157 | A United Nations report shows the mean family income for Mexican migrants to the United States is $27,000 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 25 Mexican family units reveals a mean to be $30,000 with a sample standard deviation of $10,000. Does this information disagree with the United Nations report? Apply the 0.01 significance level. |
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| m158 | A Washington, D.C., “think tank” announces the typical teenager sent 50 text messages per day in 2013. To update that estimate, you phone a sample of 12 teenagers and ask them how many text messages they sent the previous day. Their responses were:
At the .05 level, can you conclude that the mean number is greater than 50? Estimate the pvalue and describe what it tellsyou. |
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| m174 | ABC Auto Insurance classifies drivers as good, medium, or poor risks. Drivers who apply to them for insurance fall into these three groups in the proportions 30%, 50%, and 20%, respectively. The probability a “good” driver will have an accident is .01, the probability a “medium” risk driver will have an accident is .03, and the probability a “poor” driver will have an accident is .10. The company sells Mr. Brophy an insurance policy and he has an accident. What is the probability Mr. Brophy is:
a. A “good” driver?
b. A “medium” risk driver?
c. A “poor” driver? |
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| m176 | According to a government study among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $1,994. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $450.
a. What percent of the adults spend more than $2,500 per year on reading and entertainment?
b. What percent spend between $2,500 and $3,000 per year on reading and entertainment?
c. What percent spend less than $1,000 per year on reading and entertainment? |
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| m177 | According to a recent survey, Americans get a mean of 7 hours of sleep per night. A random sample of 50 students at West Virginia University revealed the mean length of time slept last night was 6 hours and 48 minutes (6.8 hours). The standard deviation of the sample was 0.9 hour. At the 5% level of significance, is it reasonable to conclude that students at West Virginia sleep less than the typical American? Compute the p-value. |
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| m178 | According to a study by the American Pet Food Dealers Association, 63% of U.S. house-holds own pets. A report is being prepared for an editorial in the San Francisco Chronicle. As a part of the editorial, a random sample of 300 households showed 210 own pets. Do these data disagree with the Pet Food Dealers Association’s data? Use a .05 level of significance. |
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| m179 | According to a study by the Federal Reserve Board, the rate charged on credit card debt is more than 14%. Listed below is the interest rate charged on a sample of 10 credit cards.
Is it reasonable to conclude the mean rate charged is greater than 14%? Use the .01 significancelevel. |
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| m180 | According to an IRS study, it takes a mean of 330 minutes for taxpayers to prepare, copy, and electronically file a 1040 tax form. This distribution of times follows the normal distribution and the standard deviation is 80 minutes. A consumer watchdog agency selects a random sample of 40 taxpayers.
a. What is the standard error of the mean in this example?
b. What is the likelihood the sample mean is greater than 320 minutes?
c. What is the likelihood the sample mean is between 320 and 350 minutes?
d. What is the likelihood the sample mean is greater than 350 minutes? |
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| m181 | According to Investment Digest ("Diversification and the Risk/Reward Relationship", Winter 1994, 1-3), the mean of the annual return for common stocks from 1926 to 1992 was 15.4%, and the standard deviation of the annual return was 24.5%. During the same 67-year time span, the mean of the annual return for long-term government bonds was 5.5%, and the standard deviation was 6.0%. The article claims that the distributions of annual returns for both common stocks and long-term government bonds are bell-shaped and approximately symmetric. Assume that these distributions are distributed as normal random variables with the means and standard deviations given previously.
a. Find the probability that the return for common stocks will be greater than 0%.
b. Find the probability that the return for common stocks will be less than 20%. |
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