"Two measured variables make a study correlational."

Unfortunately, this conflates (mistakenly treats as the same) the types of claims we can make with the types of statistical tests we can use. We pick out statistical tests based on the levels of measurement in our data, and while the measured/manipulated distinction is important for interpretation (manipulated variables allow for stronger arguments for causality), this doesn't effect our choice of test.

To make this clear, first give me an example that uses two measured variables but isn't tested using a correlation (a different test is right choice).

Second, give me an example where two variables aren't both just measured (at least one is manipulated) and yet a correlation is the proper test.

2. A student collected data on the number of large pizzas consumed, y, while x students were watching a professional football game on TV. The data from five games are given in table below. Number of students, x 2 5 6 3 4 Number of large pizzas, y 1 6 10 3 5 Please show work for full credit.

(e) Interpret your interval from part (d). (f) Calculate r2 (follow steps on page 92).

(g) Interpret r2.

(h) Compute linear correlation coecient r (follow steps on page 93).

(i) Interpret r.

If a hurricane was headed your way, would you evacuate? The headline of a press release states, "Thirty-two Percent of People on High-Risk Coast Will Refuse Evacuation Order, Survey of Hurricane Preparedness Finds." This headline was based on a survey of 5237 adults who live within 20 miles of the coast in high hurricane risk counties of eight southern states. In selecting the sample, care was taken to ensure that the sample would be representative of the population of coastal residents in these states.

(a) Use this information to estimate the proportion of coastal residents who would evacuate using a 98% confidence interval. (Round your answers to three decimal places.) (_____ ,_____ )

(b) Write a few sentences interpreting the interval and the confidence level associated with the interval. We are ____% confident that the proportion of all coastal residents who evacuate is within the confidence interval. If we were to take a large number of random samples of size 5237, ____% of the resulting confidence intervals would contain the true proportion of all coastal residents who_____evacuate.

1. Given below is a fictitious Excel output (numbers might be all made up) Answer the questions that follow. You are being tested for your ability to read the output and your skill in sensitivity analysis as taught in class.)
   

(a)        What is the objective function? You will write the algebraic version like
                          Z= 2X1+ 3X2+…etc (10)




(b)         What is the optimal solution, and the optimal value of the objective function? (15)

(b)         Can we make the following change to the RHS of the constraints as follows: (20)

                             const. 1   +20
                             const. 2    -10
                             const. 3     -5

                            
If so, what is the value of the objective function after the change. (you will show FULL work)

A mortgage specialist would like to analyze the average mortgage rates for Atlanta, Georgia. He collects data on the annual percentage rates (APR in %) for 30-year fixed loans as shown in the following table. If he is willing to assume that these rates are randomly drawn from a normally distributed population, can he conclude that the mean mortgage rate for the population exceeds 4.45%? Test the hypothesis at a 1% level of significance. (You may find it useful to reference the appropriate table: z table or t table) Financial Institution APR G Squared Financial 4.025 % Best Possible Mortgage 4.840 Hersch Financial Group 4.785 Total Mortgages Services 4.850 Wells Fargo 4.465 Quicken Loans 4.705 Amerisave 4.305 Source: MSN Money.com; data retrieved October 1, 2010. Click here for the Excel Data File a. Select the null and the alternative hypotheses. H0: µ ≥ 4.45; HA: µ < 4.45 H0: µ ≤ 4.45; HA: µ > 4.45 H0: μ = 4.45; HA: μ ≠ 4.45 b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) c. Find the p-value. 0.05 p-value < 0.10 0.025 p-value < 0.05 0.01 p-value < 0.025 p-value 0.10 p-value < 0.01 d. What is the conclusion? Do not reject H0 since the p-value is smaller than significance level. Do not reject H0 since the p-value is greater than significance level. Reject H0 since the p-value is smaller than significance level. Reject H0 since the p-value is greater than significance level. e. Make an inference at α = 0.010. The mean mortgage rate equals 4.45%. The mean mortgage rate does not equal 4.45%. The mean mortgage rate does not exceed 4.45%. The mean mortgage rate exceeds 4.45%. A mortgage specialist would like to analyze the average mortgage rates for Atlanta, Georgia. He collects data on the annual percentage rates (APR in %) for 30-year fixed loans as shown in the following table. If he is willing to assume that these rates are randomly drawn from a normally distributed population, can he conclude that the mean mortgage rate for the population exceeds 4.45%? Test the hypothesis at a 1% level of significance. (You may find it useful to reference the appropriate table: z table or t table) Financial Institution APR G Squared Financial 4.025 % Best Possible Mortgage 4.840 Hersch Financial Group 4.785 Total Mortgages Services 4.850 Wells Fargo 4.465 Quicken Loans 4.705 Amerisave 4.305 Source: MSN Money.com; data retrieved October 1, 2010. Click here for the Excel Data File a. Select the null and the alternative hypotheses. H0: µ ≥ 4.45; HA: µ < 4.45 H0: µ ≤ 4.45; HA: µ > 4.45 H0: μ = 4.45; HA: μ ≠ 4.45 b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) c. Find the p-value. 0.05 p-value < 0.10 0.025 p-value < 0.05 0.01 p-value < 0.025 p-value 0.10 p-value < 0.01 d. What is the conclusion? Do not reject H0 since the p-value is smaller than significance level. Do not reject H0 since the p-value is greater than significance level. Reject H0 since the p-value is smaller than significance level. Reject H0 since the p-value is greater than significance level. e. Make an inference at α = 0.010. The mean mortgage rate equals 4.45%. The mean mortgage rate does not equal 4.45%. The mean mortgage rate does not exceed 4.45%. The mean mortgage rate exceeds 4.45%.

Television have a lifetime of 482 hours; The Sony factory makes 10,588  in 3months. the average of a television lasting this long is  80 . what is the probability that43televisions out of the 10,588?

• What is specifically meant by sustainability, i.e., what is being sustained, in the firm’s mission or value statements?
• What are the firm’s specific sustainability goals and how are they measured?
• What specific strategies, tactics, or a practice does the firm employ to achieve its sustainability goals?
• What are the strengths and weaknesses of the company as it relates to sustainability?

A company which produces jelly beans claims that the amount, in ounces, of jelly beans in their bags is uniformly distributed on the interval 14 to 18 ounces.

(a) On average, how many ounces of jelly beans are there in a bag? What is the standard deviation?

(b) Assuming that the claim of the company is true, what is the probability that a randomly selected bag contains less than 16.25 ounces?

c) A consumer watch group wants to investigate the claim of the company. They collect a random sample of 40 bags of jelly beans and find that the average number of ounces per bag is 15.6. Assuming that the claim of the company is true, what is the probability that a sample of 40 bags has an average of less than 15.6 ounces of jelly beans per bag. Interpret this result in the context of the problem. What does this indicate about the plausibility of the claim made by the company? You must justify and explain all of your calculations and conclusions.

Problem 3) A random digit dialing telephone survey of 880 drivers asked, “Recalling the intersections on your most recent drive to work or school , were any of traffic lights red when you entered the intersections, i.e. did you run any red lights?” Of the 880 respondents, 171 admitted that yes, at least one light had been red.

a) What is the response variable? Is it categorical or quantitative?

b) Show that the normal approximation for p̂ is valid by verifying the three conditions. Include the arithmetic. (Remember that when we “assumed” that we knew π, we used nπ ≥ 10. In contrast, this problem is reality where we do not know π: we are trying to estimate π with a confidence interval. So, we use ?̂to estimate π in checking the condition.)

c) Estimate the population proportion of drivers who ran a red light on the way to work or school with a 95 percent confidence interval. (Round the standard deviation to 2 nonzero decimals. For example, if you calculate ??̂ to be 0.01234, round to 0.012.)

d) Interpret the confidence interval with a statement in the context of the problem.

Write the word or phrase that best completes each statement or answers the question.
Assume that a simple random sample has been selected from a normally distributed population and test the given
claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses,
test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that
addresses the original claim.
1) A large software company gives job applicants a test of programming ability and the
mean for that test has been 160 in the past. Twenty-five job applicants are randomly
selected from one large university and they produce a mean score and standard
deviation of 183 and 12, respectively. Use a 0.05 level of significance to test the claim that
this sample comes from a population with a mean score greater than 160. Use the
P-value method of testing hypotheses.

1. A research report indicated that in 2018, 59% of all 6^th graders owned a cell phone. A random sample of 151 6^th graders is drawn.

1. Is it appropriate to use the normal approximation for this situation? Why or why not?

2. Find the probability that the sample proportion of 6^th graders who own a cell phone is more than 64.5%. (Find P(p > 0.645)).

3. Calculate the probability that the sample proportion of 6^th graders who own a cell phone is between 54% and 66%. (Find P(.54 < p < 0.66)).

An experiment was carried out to investigate the effect of species (factor A, with I = 4) and grade (factor B, with J = 3) on breaking strength of wood specimens. One observation was made for each species—grade combination—resulting in SSA = 444.0, SSB = 424.6, and SSE = 122.4. Assume that an additive model is appropriate. (a) Test H0: α1 = α2 = α3 = α4 = 0 (no differences in true average strength due to species) versus Ha: at least one αi ≠ 0 using a level 0.05 test. Calculate the test statistic. (Round your answer to two decimal places.) f = 1 What can be said about the P-value for the test? P-value > 0.100 0.050 < P-value < 0.100 0.010 < P-value < 0.050 0.001 < P-value < 0.010 P-value < 0.001 State the conclusion in the problem context. Reject H0. The data suggests that true average strength of at least one of the species is different from the others. Fail to reject H0. The data does not suggest any difference in the true average strength due to species. Reject H0. The data does not suggest any difference in the true average strength due to species. Fail to reject H0. The data suggests that true average strength of at least one of the species is different from the others. (b) Test H0: β1 = β2 = β3 = 0 (no differences in true average strength due to grade) versus Ha: at least one βj ≠ 0 using a level 0.05 test. Calculate the test statistic. (Round your answer to two decimal places.) f = 4 What can be said about the P-value for the test? P-value > 0.100 0.050 < P-value < 0.100 0.010 < P-value < 0.050 0.001 < P-value < 0.010 P-value < 0.001 State the conclusion in the problem context. Reject H0. The data does not suggest any difference in the true average strength due to grade. Fail to reject H0. The data does not suggest any difference in the true average strength due to grade. Reject H0. The data suggests that true average strength of at least one of the grades is different from the others. Fail to reject H0. The data suggests that true average strength of at least one of the grades is different from the others.

A boat capsized and sank in a lake. Based on an assumption of a mean weight of

130130

​lb, the boat was rated to carry

7070

passengers​ (so the load limit was

9 comma 1009,100

​lb). After the boat​ sank, the assumed mean weight for similar boats was changed from

130130

lb to

172172

lb. Complete parts a and b below.

a. Assume that a similar boat is loaded with

7070

​passengers, and assume that the weights of people are normally distributed with a mean of

175.6175.6

lb and a standard deviation of

40.840.8

lb. Find the probability that the boat is overloaded because the

7070

passengers have a mean weight greater than

130130

lb.The probability is

nothing.

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

b. The boat was later rated to carry only

1717

​passengers, and the load limit was changed to

2 comma 9242,924

lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than

172172

​(so that their total weight is greater than the maximum capacity of

2 comma 9242,924

​lb).The probability is

nothing.

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

Do the new ratings appear to be safe when the boat is loaded with

1717

​passengers? Choose the correct answer below.

A.Because there is a high probability of​ overloading, the new ratings do not appear to be safe when the boat is loaded with

1717

passengers.

B.

Because the probability of overloading is lower with the new ratings than with the old​ ratings, the new ratings appear to be safe.

C.Because there is a high probability of​ overloading, the new ratings appear to be safe when the boat is loaded with

1717

passengers.

D.Because

175.6175.6

is greater than

172172​,

the new ratings do not appear to be safe when the boat is loaded with

1717

passengers.

___________________________________________________________________________________________________________________

Assume that females have pulse rates that are normally distributed with a mean of

mu equals 75.0μ=75.0

beats per minute and a standard deviation of

sigma equals 12.5σ=12.5

beats per minute. Complete parts​ (a) through​ (c) below.

a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is between

6868

beats per minute and

8282

beats per minute.The probability is

0.42460.4246.

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

b. If

1616

adult females are randomly​ selected, find the probability that they have pulse rates with a mean between

6868

beats per minute and

8282

beats per minute.The probability is

00.

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

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

A.

Since the distribution is of​ individuals, not sample​ means, the distribution is a normal distribution for any sample size.

B.

Since the distribution is of sample​ means, not​ individuals, the distribution is a normal distribution for any sample size.

C.

Since the mean pulse rate exceeds​ 30, the distribution of sample means is a normal distribution for any sample size.

D.

Since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size.

. Suppose {et : t = −1, 0, 1, . . .} is a sequence of iid random variables with mean zero and variance 1. Define a stochastic process by xt = et − 0.5et−1 + 0.5et−2, t = 1, 2, . . .

a. Is xt stationary? Show your work.

b. Is xt weakly dependent? Again, show your work.

Plz help. maybe need use SAS to solve it

For each question on a multiple-choice test, there are five possible answers of which exactly one is correct for each question. Assume there are 10 questions on the test and a student selects one answer for each question at random. Let X be the number of correct answers he or she gets.

a) How is X distributed? (Specify the values of the corresponding parameters).

b) Find P(X < 6) and P(X = 6). c) Find E(X) and V ar(X).

2. Suppose that a basketball player makes a free throw 60% of the time. Let X equal the number of free throws that this player must attempt to make a total of 3 shots. Assume independence among attempts,

a) How is X distributed? (Specify the values of the corresponding parameters)

b) Find P(X = 6).

c) Find E(X) and V ar(X). 2 3.

A factory puts biscuits into boxes of 100. The probability that a biscuit is broken is 0.03. Find the probability that a box contains 2 broken biscuits using Poisson approximation.

4. (20 pts) Let X have the p.d.f: f(x) = 3x 2 2 for −1 ≤ x ≤ 1 and f(x) = 0 for otherwise . a) Find P(X > 0.5). b) Find E(X). 3 c) Find the c.d.f F(x). d) Find π0.5. 4

5. (10 pts) Suppose that a system contains a certain type of component whose time, in years, to failure is given by X. The random variable X is modeled nicely by the exponential distribution with mean time to failure θ = 3. Find: a) P(X ≥ 4). b) Given that the component has been in operation for 2 years, find the conditional probability that it will last for at least another 4 years. 5

6. (8 pts) If X ∼ N(−10, 25), find: a) P(X ≤ 0) b) P(−15 ≤ X ≤ −5) c) P(X ≤ 20) d) π0.4.

7. (6 pts) If Z ∼ N(0, 1), find the values of z such that: a) P(Z > z) = 0.3. b) P(|Z| ≤ z) = 0.4. 6

8. (21 pts) Jim sells blueberry bushes to his customers when they are at least 18 inches tall. He wants to know how long it will take each of his blueberry bushes to grow tall enough to sell. To get an estimate of this time, he selects ten plants at random and records the number of days each one takes to grow from a seed into an 18 inch tall plant. 96, 98, 97, 101, 98, 95, 100, 95, 98, 101. Find the values of the following statistics a) Sample mean ¯x b) Sample median ˜x. c) Sample mode and sample range. d) Sample variance and sample standard deviation.