A researcher wants to evaluate the effectiveness of cognitive behavior therapy which he thinks will decrease depression scores. Prior to testing, each of n = 10 patients rated their current level of depression on a self-report survey. After attending cognitive behavior therapy for a month, a second rating is recorded. The data are as follows:

           Before   After

                                                5          2

                                                7          7

                                                10         7

                                                14         10

Do the results indicate a significant difference? Use α = .01. If so, what percent of the decrease is actually due to the therapy?

Find the following percentile for the standard normal distribution. Draw a sketch and show the R code:

a. 91st percentile

b. 9th percentile

c. 75th percentile

d. 25th percentile

e. 6th percentile

Let us consider a random variable X is the element of U(0, a) so that a has been obtained as a sample from a random variable A which follows a uniform distribution A is the element of U(0, l) with known parameter value l.

Estimates of a based on 1) the method of moments, 2) the method of maximum likelihood and 3) the Bayesian-based methods, respectively in R.

Read a data sample of r.v. X from the file sample_x.csv. Estimate a from such sample, knowing that l = 10.
i. Using only the first sample.
ii. Using only the first 5 samples.
iii. Using only the first 10 samples.
iv. Using all the samples.

sample_x.csv contains these numbers, please copy the numbers to excel file to write the estimators in R.

2.70251720663915
4.52533716919839
1.7231448657286
2.75834069244788
2.19003083976203
3.19190171690754
3.87230309952386
3.93239850995383
4.93477988922767
1.64963260015239
5.02497814716251
5.92375606054227
6.54048445225238
5.89274455816184
6.81183471748896
3.20217587502456
4.39968432805757
4.78356387178363
2.09551473182655
4.0451138126402
5.61321793564152
5.56420019695387
6.22983582402031
6.51275224747206
6.75733219590838

Please try at least for some estimators... Thank you :)

The Food Marketing Institute shows that 16% of households spend more than $100 per week on groceries. Assume the population proportion is p = 0.16 and a sample of 900 households will be selected from the population. Use z-table.

1. Calculate (), the standard error of the proportion of households spending more than $100 per week on groceries (to 4 decimals).
   
   
2. What is the probability that the sample proportion will be within +/- 0.02 of the population proportion (to 4 decimals)?
   
   
3. What is the probability that the sample proportion will be within +/- 0.02 of the population proportion for a sample of 1,300 households (to 4 decimals)?

6. There are 16 cleaning sponges in a bin at Walmart. 7 are green and the remaining 9 are blue. Suppose I randomly select 4 sponges. What is the probability that:   (Round to 4 (FOUR) decimal places.)

            a.         All four are green?

            b.         All four are blue?

            c.         2 or 3 are blue?

            d.         None are green?

            e.         3 or fewer are green?

The distribution of the number of people in line at a grocery store has a mean of 3 and a variance of 9. A sample of the numbers of people in line in 50 stores is taken.

(a) Calculate the probability that the sample mean is more than 4? Round values to four decimal places.

(b) Calculate the probability the sample mean is less than 2.5. Round answers to four decimal places.

(c) Calculate the probability that the the sample mean differs from the population mean by less than 0.5. Round answers to four decimal places.

Please help, and show step by step. Thank you.

question 12:

The risk of a portfolio can be lower than the risk of the two individual components that make up the portfolio when

Question 1:
From past experience, we know that there are 14% of freshmen, 25% of sophomores, 32% of juniors and the remaining are seniors at NAU. We also know that 21% of the freshmen, 22% of the sophomore and 11% of the juniors have taken BA 201. Also 86% of the general student population at NAU have not taken BA 201. If we randomly ask a student from NAU and find out that she has NOT taken BA201, what is the probability (in percentage) that she is a freshman? Use Excel to solve. Hint: (1) Use Excel to setup the joint probability table; (2) Notice that 21%, 22% and 11% are the conditional probabilities NOT joint probabilities; (3) just enter the value without the % sign in the answer box.

Question 2:

When two events are collectively exhaustive and mutually exclusive, which of the following are always true? (2 correct answers)

Question 4:

When there are only two possible events A and B that are mutually exclusive, which of the following is(are) always true? (2 correct answers)

Question 5:

When there are more than two events and they are statistically independent, which of the following is(are) always true? (2 correct answers)

Pete's Power Pizzas sells a chocolate/tofu filled pastry. Pete's currently sells this pastry for $13.15, and makes it for a variable cost of $5.35 per pie. A drop in cocoa prices will reduce variable cost for this product by $0.52 per pie. Pete's is thinking of reducing the pie's selling price by $0.94. By what percent must Quantity demanded increase so that Pete's just maintains its current total contribution margin (margin per unit times units sold)? (Report your answer as a percent. Report 25.5%, for example, as "25.5". Rounding: tenth of a percent.) The answer is 5.7. Please show all work to get to the answer of 5.7.

Assume you were asked to interview a researcher about the merits and weaknesses of quasi-experimental designs. Critically discuss the merits and weakness of a single group time series design

Also include in the answer the following questions with references:

1. What are the merits of each of the specific designs?
   
2. When should you use each of the specific designs?
   
3. What is the statistical analysis that is used for each of the specific designs?
   
4. What are the limitations of each of the specific designs?
   
5. What is one research question for each of the specific designs (using a topic area that you are interested in)?

In 2012, the General Social Survey asked a random sample of adults, "Compared to most people, how informed are you about politics?" Suppose that the following are the data classified by their responses to this question and their age group (the data has been modified slightly for testing purposes):

Carry out a chi-square test. Test H0: there is no relationship between age and how politically informed the person is versus Ha: there is a relationship between age and how politically informed the person is. Use α=0.01. χ2(±0.0001)= ______

P(±0.0001)= _______

a) There is no a relationship between age and how politically informed the person is

b) There is a relationship between age and how politically informed the person is

A group of 20 people have a Russian roulette party. Each person at the party plays (pulls the trigger) three times.

In between the times they re-spin the barrel. What is a box model for the fraction of people who survive the party? What is the expected value and standard error?

If they do not re-spin the barrel, what is a box model for the fraction of survivors? What is the expected value and standard error?

A consensus forecast is the average of a large number of individual analysts' forecasts. Suppose the individual forecasts for a particular interest rate are normally distributed with a mean of 6 percent and a standard deviation of 1.6 percent. A single analyst is randomly selected. Find the probability that his/her forecast is

Round your answers to 4 decimal places.

(a) At least 3.4 percent.

(b) At most 8 percent.

(c) Between 3.4 percent and 8 percent.

Listed below are the lead concentrations in ug/g measured in different traditional medicines. Use a 0.05 significance level to test the claim that the mean lead concentration for all such medicines is less than 14 ug/g.

​17.5         3.5            12.5         9                4                9.5            20.5         10             10.5         21

1. Thirty years ago, the mean number of rides that were disabled (broken) for more than two

hours at Disneyland was 10.2 per month. The current CEO, Bob Iger, believes that number has

gone down and randomly selects 11 months from the past three years and checks on the number

of disabled rides. If the mean has decreased, he will give the members of the maintenance staff a

$50K bonus this year. If not, they will all be immediately fired.

14

10

5

6

8

10

10

8

9

9

7

a. At the 10% significance level, do the data provide evidence that the mean number of disabled

rides per month has decreased?

b. In the context of this problem, describe Type I and Type II errors and their consequences.

Which one, in your opinion, is more severe?

Type I:

Type II: