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free/or 0.5$ |
| m143 | A study regarding the relationship between age and the amount of pressure sales personnel feel in relation to their jobs revealed the following sample information. At the .01 significance level, is there a relationship between job pressure andage? |
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| m144 | A study was conducted to determine if there was a difference in the humor content in British and American trade magazine advertisements. In an independent random sample of 270 American trade magazine advertisements, 56 were humorous. An independent random sample of 203 British trade magazines contained 52 humorous ads. Do these data provide evidence at the .05 significance level that there is a difference in the proportion of humorous ads in British versus American trade magazines? |
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| m145 | A suburban hotel derives its revenue from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied?
Use a statistical software package to answer the following questions.
a. Does the revenue seem to increase as the number of occupied rooms increases? Draw a scatter diagram to support your conclusion.
b. Determine the correlation coefficient between the two variables. Interpret the value.
c. Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the .10 significance level.
d. What percent of the variation in revenue in the restaurant is accounted for by the numer of roomsoccupied? |
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| 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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| m159 | a. If c: [0, 2π] x [-1, 1] -> c: [0 , 2π] x [-1, 1] -> R3 is defined by c (u,v) = (2 eos (u) + vsin (u/2) eos (u),
2sin (u) + vsin (u/2) sin (u), veos (u/2)). |
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| m160 | a. If C is a set of content 0, show that the boundary of C also has content 0.
b. Give an example of a bounded set C of measure 0 such that the boundary of C does not have measure 0. |
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| m161 | a. If f: |a, b|-> R is non-negative and the graph of f in the x,y -plane is revolved around the -axis in R3 to yield a surface M, show that the area of M is |
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| m162 | a. If f is a differentiable vector field on M C Rn, show that there is an open set AЭM and a differentiable vector field F on A with F(x) = F (x) for xЄM.
b. If M is closed, show that we can choose A = Rn. |
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