In a large population of college-educated adults, the mean IQ is 118 with a standard deviation of 20. Suppose 200 adults from this population are randomly selected for a market research campaign. The probability that the sample mean IQ is greater than 120 is Select one: a. 0.0001. b. 0.0790. c. 0.1230. d. 0.9210. e. Cannot be determined

(a) Suppose you are given the following (x, y) data pairs. x 1 2 5 y 4 3 6 Find the least-squares equation for these data (rounded to three digits after the decimal). ŷ = + x (b) Now suppose you are given these (x, y) data pairs. x 4 3 6 y 1 2 5 Find the least-squares equation for these data (rounded to three digits after the decimal). ŷ = + x (c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair? Yes No Correct: Your answer is correct. (d) Solve your answer from part (a) for x (rounded to three digits after the decimal). x = + y Do you get the least-squares equation of part (b) with the symbols x and y exchanged? Yes No Correct: Your answer is correct. (e) In general, suppose we have the least-squares equation y = a + bx for a set of data pairs (x, y). If we solve this equation for x, will we necessarily get the least-squares equation for the set of data pairs (y, x), (with x and y exchanged)? Explain using parts (a) through (d). In general, switching x and y values produces a different least-squares equation. In general, switching x and y values produces the same least-squares equation. Switching x and y values sometimes produces the same least-squares equation and sometimes it is different. Correct: Your answer is correct.

6. The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are 39,35,15,14. Assume that samples of size n=2 are randomly selected with replacement from this population of four values

a. After identifying the 16 different possible samples and finding the mean of each​ sample, construct a table representing the sampling distribution of the sample mean. In the​ table, values of the sample mean that are the same have been combined.

X	Probability
39
37
35
27
26.5

(Type integers or​ fractions.)

X	Probability
25
24.5
15
14.5
14

(Type integers or​ fractions.)

b. Compare the mean of the population to the mean of the sampling distribution of the sample mean.

The mean of the​ population, ____ is, (greater than/less than/equal to) the mean of the sample​ means, ___.

​(Round to two decimal places as​ needed.)

c. Do the sample means target the value of the population​ mean? In​ general, do sample means make good estimates of population​ means? Why or why​ not?

The sample means (Do Not target/target) the population mean. In​ general, sample means (Do/ Do Not) make good estimates of population means because the mean is (an unbiased/ a biased) estimator

Must Show Work

.  Based on her own experiences in court, a prosecutor believes that some judges provide more severe punishments than other judges for people convicted of domestic violence.  Five of the most recent domestic violence sentences (in years) handed down by three judges are recorded below.

Judge 1	Judge 2	Judge 3
1	3	1
1	2	5
3	4	2
2	3	1
2	4	1

Using this information, test the null hypothesis at the .05 level of significance that judges do not vary in the sentence lengths imposed on individuals convicted of domestic violence.  In so doing, please: (1) identify the research and null hypotheses, (2) the critical value needed to reject the null, (3) the decision that you made upon analyzing the data, and (4) the conclusion you have drawn based on the decision you have made.

2. A food processing plant typically contain fungus spores. If the ventilation system is not adequate, this can have a serious effect of the health of employees. To determine the amount of spores present, random air samples are pumped to a certain plate, and the number of "colony-forming units (CFUs)" are determined after time allowed for incubation. The data from the room of a plant that slaughters 35,000 turkeys per day, which are obtained during the four seasons of the year, is given below. The units are in CFUs per cubic meter.

Fall Winter Spring Summer

1231 384 2105 3175

1254 104 701 2526

1088 97 842 1090

1124    401 1243 1987

a) Examine the data using exploratory data analysis tools. Create at least one graph comparing means.

b) Perform an -way ANOVA to determine is the effect of the season is statistically significant. Use the four-step method. Be sure to give a practical conclusion. Assume the populations are normally distributed and the variances are roughly equal. Copy and paste the results of the test into your Word document.

Run a regression analysis on the following bivariate set of data with y as the response variable. x y 37.2 26.9 66.2 41.4 80.9 37.6 83.7 45 55 31.2 46.3 29.1 82 44.1 71.6 36.1 54.7 29.3 56.4 33.8 Predict what value (on average) for the response variable will be obtained from a value of 45.1 as the explanatory variable. Use a significance level of α = 0.05 to assess the strength of the linear correlation. What is the predicted response value? (Report answer accurate to one decimal place.)

7. Assume a population of 46​, 51​, 53​, and 59. Assume that samples of size n=2 are randomly selected with replacement from the population. Listed below are the sixteen different samples. Complete parts

​(a​) through (c​).

Sample x1        x2

1          46        46

2          46        51

3          46        53

4          46        59

5          51        46

6          51        51

7          51        53

8          51        59

9          53        46

10        53        51

11        53        53

12        53        59

13        59        46

14        59        51

15        59        53

16. 59        59

a.Find the median of each of the sixteen​ samples, then summarize the sampling distribution of the medians in the format of a table representing the probability distribution of the distinct median values. Use ascending order of the sample medians.

Social Median	Probability	Social Median	Probability
(69,92,46)		(78.5,105,52.5)
(71.5,97,48.5)		(80.5,53,106)
(99,49.5,74)		(110,55,82)
(76,102,51)		(56,84.5,112)
(76.5,52,104)		(88.5,118,59)

                   ​(Type integers or simplified fractions. Use ascending order of the sample​ medians.)

b. Compare the population median to the mean of the sample medians. Choose the correct answer below.

A. The population median is equal to the mean of the sample medians.

B. The population median is not equal to the mean of the sample medians​ (it is also not half or double the mean of the sample​ medians).

C. The population median is equal to double the mean of the sample medians.

D. The population median is equal to half of the mean of the sample medians.

c. Do the sample medians target the value of the population​ median? In​ general, do sample medians make unbiased estimators of population​ medians? Why or why​ not?

A. The sample medians target the population​ median, so sample medians are unbiased​ estimators, because the mean of the sample medians equals the population median.

B. The sample medians target the population​ median, so sample medians are biased​ estimators, because the mean of the sample medians equals the population median.

C. The sample medians do not target the population​ median, so sample medians are unbiased​ estimators, because the mean of the sample medians does not equal the population median.

D. The sample medians do not target the population​ median, so sample medians are biased​ estimators, because the mean of the sample medians does not equal the population median.

1. A population of values has a normal distribution with μ=72μ=72 and σ=3.1σ=3.1. You intend to draw a random sample of size n=154n=154.

Find the probability that a single randomly selected value is between 71.3 and 71.7.
P(71.3 < X < 71.7) =

Find the probability that a sample of size n=154n=154 is randomly selected with a mean between 71.3 and 71.7.
P(71.3 < M < 71.7) =

Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

2.

In a recent year, the Better Business Bureau settled 75% of complaints they received. (Source: USA Today, March 2, 2009) You have been hired by the Bureau to investigate complaints this year involving computer stores. You plan to select a random sample of complaints to estimate the proportion of complaints the Bureau is able to settle. Assume the population proportion of complaints settled for the computer stores is the 0.75, as mentioned above. Suppose your sample size is 278. What is the probability that the sample proportion will be at least 5 percent more than the population proportion?

Note: You should carefully round any z-values you calculate to at least 4 decimal places to match wamap's approach and calculations.

Answer =

(Enter your answer as a number accurate to 4 decimal places.)

3.

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 165000 dollars. Assume the standard deviation is 32000 dollars. Suppose you take a simple random sample of 90 graduates.

Find the probability that a single randomly selected salary that doesn't exceed 169000 dollars.
Answer =

Find the probability that a sample of size n=90n=90 is randomly selected with a mean that that doesn't exceed 169000 dollars.
Answer =

Enter your answers as numbers accurate to 4 decimal places.

Thank You

Question 1

A university claims that the average cost of books per student, per semester is $300. A group of students believes that the actual mean is higher than this. They take a random sample of 100 students and calculate the sample mean to be $345 with a standard deviation of $200.

a)         Perform a z-test to see if the students are correct, that the true mean is greater than $300 using α = 0.05. Specify the hypotheses, test statistic, decision rule and conclusion.

b) Calculate the p-value for the test in part a). Does this agree with your answer to part a)? Explain why or why not.

c)   Calculate a 90% confidence interval for µ. Does this agree with your answer to part a)? Explain why or why not.

Identify the level of measurement of each of the following variables: a)The amount of resistance a suspect displays toward the police, measured as not resistant, somewhat resistant, or very resistant B)The number of times someone has shoplifted in her or his life C)The number of times someone has shoplifted, measured as 0–2, 3–5, or 6 or more D)The type of attorney a criminal defendant has at trial, measured as privately retained or publicly funded E)In a sample of juvenile delinquents, whether or not those juveniles have substance abuse disorders F)Prosecutors’ charging decisions, measured as filed charges and did not file charges G)In a sample of offenders sentenced to prison, the number of days in their sentences

2. Identify the level of measurement for the following variables from the 2010 General Social Survey data:

a. Sex, b. Race, c. Highest educational degree earned,d. Hours worked per week, and e. Age at first marriage

1. Identify whether each of the situations below is a one-tailed or two-tailed test. Next identify the dependent variable. Then write the research and null hypothesis in symbols (i.e. H1: µ_{. . .} =/> etc . . .). You should clearly identify the two groups using subscripts after each µ.
   1. You are interested in finding out whether the average household income of Washington residents is different from the national average for households in other states.
   2. You hypothesize that students at liberal arts colleges attend more parties per month than students in state universities.
   3. An economist believes that the average income of elderly women is smaller than the average income of elderly men.
   4. Is there a difference in the amount of time students living on campus and students living off campus devote to studying each week?
   5. Math scores for a group of third graders enrolled in an accelerated math program are predicted to be higher than the scores for non-enrolled third graders.
   6. The number of times someone gets sick each year is predicted to be lower for adults who own dogs than for non-dog owners.

1) For the following data values below, construct a 90% confidence interval if the sample mean is known to be 0.719 and the standard deviation is 0.366. (Round to the nearest thousandth) (Type your answer in using parentheses! Use a comma when inputing your answers! Do not type any unnecessary spaces! List your answers in ascending order!) for example: (0.45,0.78) 0.56, 0.75, 0.10, 0.95, 1.25, 0.54, 0.88

2) For the following data values below, construct a 98% confidence interval if the sample mean is known to be 9.808 and the population standard deviation is 5.013. (Round to the nearest thousandth) (Type your answer in using parentheses! Use a comma when inputing your answers! Do not type any unnecessary spaces! List your answers in ascending order!) for example: (0.45,0.78) 6.6, 2.2, 18.5, 7.0, 13.7, 5.4, 5.3, 5.9, 4.7, 14.5 2.0, 14.8, 8.1, 18.6, 4.5, 17.7, 15.9, 15.1, 8.6, 5.2 15.3, 5.6, 10.0, 8.2, 8.3, 9.9, 13.7, 8.5, 8.2, 7.9 17.2, 6.1, 13.7, 5.7, 6.0, 17.3, 4.2, 14.7, 15.2, 3.3 3.2, 9.1, 8.0, 18.9, 14.2, 5.1, 5.7, 16.4, 10.1, 6.4

3)In a randomized controlled trial in Kenya, insecticide treated bednets were tested as a way to reduce malaria. Among 343 infants using bednets, 15 developed malaria. Among 294 infants not using bednets, 27 developed malaria. Want to use a 0.01 significance level to test the claim that the incidence of malaria is lower for infants using bednets. Find the test statistic. (Round to the nearest hundredth) (ONLY TYPE IN THE NUMBER!)

4)State the conclusion whether or not to REJECT or FAIL TO REJECT the null hypotheses.(Check your spelling!) The original claim: The percentage of of M&Ms is greater than 5%. The hypothesis test results in a p-value of 0.0010. a=0.05

Assume that student are to be sperated into a group with IQ scores in the bottom 30%, a second group with scores in the middle 40%, and a third group with scores in the top 30%. The Wechsler Adult Intelligence Scale yields an IQ score obtained through a test, and the scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the IQ score that seperates the three groups.

Problem 2

1. When Alice gets stressed out about her classes, she plays a game in which she rolls a pair of dice and if the sum of the two numbers is at least 10, she “wins.” For each win, she gives herself a dollar for ice cream.

(a) The night before the final exam, Alice will play this game 10 times. What is the probability that she will win herself at least $3 for ice cream?

(b) Alice teaches this game to Bob, who is taking another course. The night before his final exam, Bob plays the game 10 times. But Bob really likes ice cream, and he’s really stressed out, so he plays with a special pair of dice that are weighted so that p(5) = p(6) = 2p(4) = 2p(3) = 2p(2) = 2p(1). (In other words, he is twice as likely to roll a 5 or a 6 than any other number.) What is the probability that Bob will win himself at least $3 for ice cream?

(c) How many times should Alice play her game to ensure that she will have at least a 50% chance of winning at least $5? (NOTE: Alice will play with the original version in (a) not Bob’s cheating version in (b).) (HINT: This may be rather tedious to calculate by hand, so you may want to write a short program to calculate it. If you do, attach an image of your code as well as a short explanation of your procedure and the final answer.)