Marxe School of Public and International Affairs (SPIA) wants to find out about the careers of its MPA graduates. The dean mails questionnaires to 500 randomly selected Alumni. Analysis of the sample of 500 alumni shows that the average income is $65,000. The average age is 35 years. The proportion working in non-profit is 76%.

Deduce the following information:

1)(1 Points)The population refers to:

2)(1 Points)The sample refers to:

3)(3 Points)The threevariables are (Hint: remember that the variables are the questions or the respondents’ attributes being asked in the questionnaires, such as age):

4)(3 Points)The three sample statistics refer to:

(Note: Do not only give the numbers. Provide descriptions of what the numbers refer to. To give an example that is not in this question - A sample statistic could be the average number of hours worked per week by the sampled workers which is 38.5 hours per week.)

5)(3 Points)The three population parameters refer to:

Refer to Table 22-13. In a pairwise election between Mexico and Ecuador and then a second election between the winner and Costa Rica, which countries are chosen?

1. 7.75 p. 428

Salaries for teachers in a particular elementary school district are normally distributed with a mean of $44,000 and a standard deviation of $6,500. We randomly survey ten teachers from that district.

a. In words, X = ______________

b. X ~ _____(_____,_____)

c. In words, ΣX = _____________

d. ΣX ~ _____(_____,_____)

e. Find the probability that the teachers earn a total of over $400,000.

f. Find the 90th percentile for an individual teacher's salary.

g. Find the 90th percentile for the sum of ten teachers' salary.
h. If we surveyed 70 teachers instead of ten, graphically, how would that change the distribution in part d?

i. If each of the 70 teachers received a $3,000 raise, graphically, how would that change the distribution in part b?

2. 7.90 p. 431

The average length of a maternity stay in a U.S. hospital is said to be 2.4 days with a standard deviation of 0.9 days. We randomly survey 80 women who recently bore children in a U.S. hospital.

a. In words, X = _____________

b. In words, X ¯ = ___________________

c. X ¯ ~ _____(_____,_____)

d. In words, ΣX = _______________

e. ΣX ~ _____(_____,_____)

f. Is it likely that an individual stayed more than five days in the hospital? Why or why not?

g. Is it likely that the average stay for the 80 women was more than five days? Why or why not? h. Which is more likely:

i. An individual stayed more than five days.

ii. the average stay of 80 women was more than five days.

i. If we were to sum up the women’s stays, is it likely that, collectively they spent more than a year in the hospital? Why or why not?

(3) Finding Dory Coral Reef communities are home to one-quarter of all marine plants and animals worldwide. These reef support large fisheries by providing breeding grounds and safe havens for young fish of many species. Coral reefs are seawalls (protecting shorelines from tides, storm-surges, and hurricanes as well as produce the limestone and sand of which beaches are made), Marine scientists say that a tenth of the world’s reef systems have been destroyed in recent times. At current rates of loss, almost three-quarters of the reefs could be gone in 30 years. A particular lab studies corals and the diseases that affect them. Dr. Drew Harvell and his lab sampled sea fans at 19 randomly selected reefs along the Yucatan peninsula and diagnosed whether the animals (the sea fans) were affected by aspergillosis1 . In specimens collected at a depth of 40 feet at the Las Redes Reef in Akumal, Mexico, scientists found that 52% of the 104 sampled sea fans were infected with aspergillosis.

(a) What are the mean (proportion, p) and standard deviation of the sampling distribution of the sample proportion (mean (p) and sepˆ) of infected sea fans? What should the distribution look like (think of the definition of CLT)?

(b) What is probability that the sample proportion of infected sea fans is less than 50% (that is find P(ˆp < .5))?

(c) What is probability that the sample proportion of infected sea fans is between 40 and 60%?

(4) There is no Dana, only Zeul (Who you gonna call?) In November of 2005 the Harris Poll asked 889 randomly selected US adults, “Do you believe in ghosts?” 29% said they did.

(a) In constructing confidence intervals, would we use z ? or t ? in this situation? Briefly explain why you would use one instead of the other.

(b) Estimate p, the true proportion of US adults that believe in ghosts, with 90% confidence. Interpret the interval in context of the data.

(c) Suppose, using the information from the survey (the 29% that believe in ghosts) that a new survey is to be taken and the new bound is to be 2%. What sample size will be required?

(d) Suppose that we know nothing of any prior results from this study (thus have no estimate for the proportion of those US adults that believe in ghosts). What proportion should we use for the estimation? What sample size do we need with no prior information? Why is it different than the sample size from part (c).

(5) Got Milk? Although most of us buy milk by the quart or gallon, farmers (at least in the US) measure daily production in pounds (lbs.). Ayrshire cows have a known standard deviation of 6 pounds and average 47 pounds of milk per day. Jersey cows have a known standard deviation of 5 pounds and the mean daily production is 43 pounds. Assume that the distribution of daily milk production is approximately normal and suppose one farm has 20 of each type of cow (20 Ayrshire and 20 Jersey).

(a) In constructing confidence intervals, would we use z ? or t ? in this situation? Briefly explain why you would use one instead of the other.

(b) Estimate µ, the true mean daily milk production of both Ayrshire and Jersey cows (you will have 2 CIs), with 95% confidence. Interpret.

(c) Suppose the next time the farmer takes a sample of Ayrshire cows, he wants to make sure the bound is 2. Maintaining 95% confidence, what sample size will be required for the new sample?

(6) Using the t table Find the degrees of freedom (df) and the value of t ? for the given sample size and confidence level or significance level (α). [Hint: if it states ‘CL’, that means that α is divided by 2. If it says ‘α = ’, then you do not divide α by 2.]

(a) n = 6,CL = 90%

(b) n = 21,CL = 98%

(c) n = 29,CL = 95%

(d) n = 12,CL = 99%

(e) n = 6,α = 0.10

(f) n = 21,α = 0.01

(g) n = 40,α = 0.05

(7) It ain’t easy bein’ green A dealer in recycled paper places empty trailers at various sites. The trailers are gradually filled by individuals who bring in old newspapers and magazines, and are picked up on several schedules. One such schedule involves pickup every second week. This schedule is desirable if the average amount of recycled paper is more than 1600 cubic feet per 2-week period. Below is a copy of the dealer’s records for eighteen 2-week periods show the following volumes (in cubic feet) at a particular site; the mean and standard deviation are as follows: X¯ = 1721.6 and s = 154.5

(a) In constructing confidence intervals, would we use z ? or t ? in this situation? Briefly explain why you would use one instead of the other.

(b) Estimate the true mean weight of recycled paper with 95% confidence. Interpret.

recycle=c(1935,1556,1752,1969,1804,1842,1994,1810,1827,1725,2003,1499,1809,1795,1622,1620,1777,2035)

(8) 9.7 p. 535

In a population of fish, approximately 42% are female. A test is conducted to see if, in fact, the proportion is less. State the null and alternative hypotheses

(9) 9.9 p. 535

A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.4 years with a standard deviation of 6.3 years. If you were conducting a hypothesis test to determine if the population mean time on death row could likely be 15 years, what would the null and alternative hypotheses be?

a. H_0: __________

b. H_a: __________

(10) 9.62 p. 538

Some of the following statements refer to the null hypothesis, some to the alternate hypothesis. State the null hypothesis, H0, and the alternative hypothesis. Ha, in terms of the appropriate parameter (μ or p).

a. The mean number of years Americans work before retiring is 34.

b. At most 60% of Americans vote in presidential elections.

c. The mean starting salary for San Jose State University graduates is at least $100,000 per year.

d. Twenty-nine percent of high school seniors get drunk each month.

e. Fewer than 5% of adults ride the bus to work in Los Angeles.

f. The mean number of cars a person owns in her lifetime is not more than ten.

g. About half of Americans prefer to live away from cities, given the choice.

h. Europeans have a mean paid vacation each year of six weeks.

i. The chance of developing breast cancer is under 11% for women.

j. Private universities' mean tuition cost is more than $20,000 per year

At the beginning of each football season, the coaching staff at Vista High School must vote to decide which players to select for the team. They use the weighted voting system {7: 6, 5, 1}. In this voting system, the head coach A has a weight of 6, the assistant coach B has a weight of 5, and the junior varsity coach C has a weight of 1. Compute the Banzhaf power index for each of the coaches. (Round your answers to the nearest hundredth.)

BPI(A) =

BPI(B) =

BPI(C) =

1. A study to determine how often kindergarteners miss school due to illness is made. The following hypotheses are given: 2 2 0 1 2 2 2 1 1 2 : : H H       A random sample of six observations from the first population resulted in a standard deviation of 10. A random sample of eight from the second population showed a standard deviation of 12. AT the 0.01 significance level, is there more variation in the first population? (A) The critical value is:______________ (6) (B) The test-statistic is:________________ (6) (C) Circle the correct response: Decision: Reject H0 or Do not Reject H0

The wisdom of depending on International Medical School Graduates (IMGs) to fill gaps in physician supply, while US medical schools hold class size constant, is questionable. In addition, the aging of the physician workforce, the decreasing hours worked by both physicians in practice and physicians in residency, and a 20 percent reduction in the effort of the increasing proportion of female physicians, will result in a significant decrease in the “effective” supply of physicians. Should the gap be filled by a major substitution of nurse practitioners, physician assistants, chiropractors, acupuncturists, and others, or are there alternatives?

Vitamin C is becoming an issue. A researcher thinks that high school students are getting enough. The researcher does a study of many local schools. The table shows the number of student who got the daily, recommended allowance of vitamin C. Can you conclude that the numbers of students who got the daily, recommended allowance of vitamin C is the same for all grades? Test the claim at the level of significance of .05.

1. You sample 16 students in your school, and they average 13 hours of TV a week. Assume​ σ​ =3. Find a 99% Confidence Interval

2. A hardware manufacturer produces bolts used to assemble various machines. Assume that the diameter of bolts produced by this manufacturer has an unknown population mean and the standard deviation is 0.1 mm. Suppose the average diameter of a simple random sample of 75 bolts is 5.12 mm. Calculate the margin of error of a 95% confidence interval for the mean then determine the 95% confidence interval

3. You want to rent an unfurnished one-bedroom apartment in Boston next year. The mean monthly rent for a simple random sample of 30 apartments advertised in the local newspaper is $1,450. The standard deviation of the population is $220. Find a 99% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community.

4. An appliance manufacturer stockpiles washers and dryers in a large warehouse for shipment to retail stores. Sometimes, handling them the appliances get damaged. Even though the damage may be minor, the company must sell those machines at drastically reduced prices. One day an inspector randomly checks 50 washers and finds that 5 of them have scratches or dents. Compute a 95% confidence interval for the proportion of appliances from this manufacturer that get damaged during shipment.

5. You are testing chocolate chip cookies to estimate the mean number of chips per cookie.You sample 20 cookies and you find a sample mean of 10 chips per cookie. Assume ​σ​ = 2 .Find a 99% confidence interval.

6. If 64% of a sample of 550 people leaving a shopping mall claims to have spent over $25, determine a 99% confidence interval estimate for the proportion of shopping mall customers who spend over $25.

7. In a random sample of machine parts, 18 out of 225 were damaged in a shipment. Establish a 95% confidence interval estimate for the proportion of damaged machine parts in shipment.

8. A travel agent wants to estimate the proportion of vacationers who plan to travel outside the United States in the next 12 months. A random sample of 150 vacationers revealed that 45 had plans for foreign travel in that time frame.

a) Suppose (at the 95% con fidence level) you need to have a margin of error no more than 4 percentage points. How many vacationers would you have to sample? (Use the sample proportion you calculated in part (a) as an estimate of ^p. )

b) Suppose (at the 95% con dence level) you need to have a margin of error no more than 4 percentage points, but you have no estimate of ^p. How many vacationers would you have to sample?

A sample poll of 100 voters chosen at random from all voters in a given school district indicated that 53% of them were in favor of a 1% increase in property taxes in order to provide funds to hire more teachers.

          a.       Find the 95% confidence interval for the population proportion of voters supporting the property tax

                    hike?

          b.       Can we be confident that the tax hike will pass given your results in part (a)? Explain.

          c.       What is the required sample size needed to get the margin of error within ±2%?

In general, high school and college students are the most pathologically sleep-deprived segment of the population. Their alertness during the day is on par with that of untreated narcoleptics and those with untreated sleep apnea. Not surprisingly, teens are also 71 percent more likely to drive drowsy and/or fall asleep at the wheel compared to other age groups. (Males under the age of twenty-six are particularly at risk.) The accompanying data set represents the number of hours 25 college students at a small college in the northeastern United States slept and is from a random sample. Enter this data into C1 of Minitab Express. 6 7 6 7 6 7 7 7 8 6 6 6 8 8 8 5 4 6 7 8 5 8 7 6 7 For the analyses that follow, we shall use 90%, 95%, and 99% as the confidence levels for the confidence interval. 5% as the level of significance (?) for the hypothesis test. 7 hours sleep as the null hypothesis (according to The Sleep Foundation). Use Minitab Express to: (i) create a boxplot – GRAPHS, Boxplot - and (ii) normal probability plot – GRAPHS, Probability Plot, and (iii) calculate descriptive statistics - STATISTICS, Describe, Descriptive Statistics. Under the “Descriptive Statistics” dialog window, click on the Statistics tab and check only Mean, SE of mean, Standard deviation, and N. Include these with the submission of your project

Use Minitab Express to: (i) create a boxplot – GRAPHS, Boxplot - and (ii) normal probability plot – GRAPHS, Probability Plot, and (iii) calculate descriptive statistics - STATISTICS, Describe, Descriptive Statistics. Under the “Descriptive Statistics” dialog window, click on the Statistics tab and check only Mean, SE of mean, Standard deviation, and N. Include these with the submission of your project.