I need solution and formula as clear.Otherwise , I will have to report the answer.

Assume that X and Y has a continuous joint p.d.f. as 28x2y3 in 0<y<x<1 interval. Otherwise the joint p.d.f. is equal to 0.

a.Calculate Var(X)

b.Calculate P(X< 0.1)

c.Calculate P(X> 0.1)

d.Calculate P(X>2)

e.Calculate P(-2<X<0.1)

A variable of a population has a mean  and a standard deviation .

a. The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean and standard deviation of

A manufacturer wants to compare the number of defects on the day shift with the number on the evening shift. A sample of production from recent shifts showed the following defects:

Day Shift​​: 6​ 9​ 8​ 7​ 10​ 8

Evening Shift: ​​9​ 11​ 8​ 12​ 10​ 13​ 15​ 10

The objective is to determine whether the mean number of defects on the night shift is greater than the mean number on the day shift at the 95% confidence level.

a) State the null and alternate hypotheses.

b) What is the level of significance?

c) What is the test statistic?

d) What is the decision rule?

e) Use the Excel Data Analysis pack to analyze the problem. Include the output with your answer. (Note: You may calculate by hand if you prefer).

f) What is your conclusion?  Explain.

g) Does the decision change at the 99% confidence level?

Research Design: The basic research design is correlational, that is, two sets of measurements are obtained from clients who appear at the clinic stating that they desire assistance from their staff to quit smoking. One measurement is the self-report of the current average number of cigarettes (or the equivalent) smoked per day, and the other measure is data from a checklist of anxiety-linked behaviors reportedly experienced during the past 30 days. These two measures will be recorded in an Excel Spreadsheet and analyzed using Correlation and Regression. Measurements: The first time each client appears at the clinic for treatment, the client will be asked to complete an “intake survey” which consists of providing information on the client’s name, address, and telephone number (optional), a self-report on the client’s non-smoking goals, a self-assessment of the current, approximate average number of cigarettes (or the equivalent) smoked per day, and checking off the symptoms they have experienced in the past 30, days such as:

___Nailbiting ___Episodes of withdrawal

___Hard Breathing ___Excessive talking

___Trembling hands ___Lack of beauty in life’s fun

___Tics ___Rapid speech

___Outbreaks of anger ___Heartbeat flutters

___Excessive blinking ___Episodes of general discomfort

___Constant nervousness ___Upset stomach

___Loss of sleep ___Frequent lapses in concentration ___Pain in back and/or shoulders

Research Questions :

1. Is there a significant correlation between smoking frequency and reported symptoms of anxiety?

2. Is the regression equation for predicting the number anxiety symptoms from the number of cigarettes smoked per day a practical way to forecast anxiety among the Quit Smoking Now! Clinic client population? (That is, is R Squared at least .50?)

1. Family transportation costs are usually higher than most people believe because those costs include car payments, insurance, fuel costs, repairs, parking, and public transportation. Twenty randomly selected families in four major cities are asked to use their records to estimate a monthly figure for transportation cost.
   1. Use the data obtained and ANOVA to test whether there is a significant difference in monthly transportation costs for families living in these cities. Assume that α = .05. Report a p-value and interpret the results of the statistical test.
   2. Use α= 0.05, and construct confidence intervals for all pairs of differences between means. Which of these differences, if any, are statistically significant at the selected significance level?

Suppose we are comparing average scores on a test for two groups that used different study techniques. The null hypothesis is that μ1 - μ2 = 0 A. If μ1 = 84 and μ2 = 80, which of the following are true (select all that apply)?

If we fail to reject H0, we are making the correct decision

If we fail to reject H0, we are committing a Type I error

If we fail to reject H0, we are committing a Type II error

If we reject H0, we making the correct decision

If we reject H0, we are committing a Type I error

If we reject H0, we are committing a Type II error

B.

If μ1 = 76 and μ2 = 76, which of the following are true (select all that apply)?

If we fail to reject H0, we are making the correct decision

If we fail to reject H0, we are committing a Type I error

If we fail to reject H0, we are committing a Type II error

If we reject H0, we making the correct decision

If we reject H0, we are committing a Type I error

If we reject H0, we are committing a Type II error

Based on recent data, there are on average 1.3 days per winter where snowfall reaches more than 6 inches in Central Park, New York City. We’ll call these “snow days”.

Assume that there were more than 2 “snow days” this winter. What is the chance that exactly 4 such days occur?

In a survey of 3937 adults, 706 say that they have seen a ghost. Construct a​ 99% confidence interval for the population proportion. Interpret the results.

In a survey of 2311 adults, 727 say they believe in UFOs. Find the 99% confidence interval for the population proportion of adults who believe in UFOs.

People with albinism have little pigment in their skin, hair, and eyes. The gene that governs albinism has two forms (alleles), which are denoted by a and A. Each person has a pair of these genes, one inherited by from each parent. A child inherits one of each parent’s two alleles, independently with probability 0.5. Albinism is a recessive trait, so a person is albino only of the inherited pair is aa.

Hint: Make a probability tree.

1. Beth’s parents are not albino but she has an albino brother. What types must Beth’s parent’s be AA? Aa? aa?
2. Which of the types AA, Aa, aa, could a child of Beth’s parents have? What is the probability for each type?
3. Beth is not albino. What are the conditional probabilities for Beth’s possible genetic types?

Assume that the probabilities for Beth’s genetic types are given by part (c) above. Beth marries Bob who is albino.

4. What is the conditional probability that a child of Beth and Bob is non-albino if Beth is of type Aa?
5. What is the conditional probability that a child of Beth and Bob is non-albino if Beth is of type AA?
6. Beth and Bob’s first child is non-albino. What is the conditional probability that Beth is of type AA?

A gambler plays a sequence of games that she either wins or loses. The outcomes of the games are independent, and the probability that the gambler wins is 2/3. The gambler stops playing as soon as she either has won a total of 2 games or has lost a total of 3 games. Let T be the number of games played by the gambler.

1. Find the probability mass function of T.
2. Find the mean of T.
3. Find the standard deviation of T.

Given a binomial distribution with n = 6 and p = 0.55​, obtain the values below. a. the mean b. the standard deviation c. the probability that the number of successes is larger than the mean d. the probability that the number of successes is within plus or minus 2 standard deviations of the mean

A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. Her realtor friend informs them that the last 26 houses that sold in their neighborhood took an average time of 75 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 8 days. [You may find it useful to reference the z table.]

a. What assumption regarding the population is necessary for making an interval estimate for the population mean?

• Assume that the central limit theorem applies.

• Assume that the population has a normal distribution.

b. Construct the 90% confidence interval for the mean sale time for all homes in the neighborhood. (Round intermediate calculations to at least 4 decimal places. Round "z" value to 3 decimal places and final answers to 2 decimal places.)

1) A. In a Rasmussen Poll of 1020 adults in July 2010, 512 of those polled said that schools should ban sugary snacks and soft drinks. Do a majority of adults support a ban on sugary snacks and soft drinks? Perform a hypothesis test using a significance level of 10%

B. Historically, the percentage of U.S. residents who support stricter gun control laws been 54%.A recent Gallup Poll of 1011 people showed 499 in favor of stricter gun 10% control laws. Assume the poll was given to a random sample of people. Test the claim that the proportion of those favoring stricter gun control has fallen. Perform a hypothesis test, using a significance level of 1%

How do I conduct a chi square analysis to test in SPSS using the nonparametric test under the analyze tab

The PACE project at the University of Wisconsin in Madison deals with problems associated with high-risk drinking on college campuses. Based on random samples, the study states that the percentage of UW students who reported bingeing at least three times within the past two weeks was 42.2% in 1999 (n = 334) and 21.2% in 2009 (n = 843). Test that the proportion of students reporting bingeing in 1999 is different from the proportion of students reporting bingeing in 2009 at the 10% significance level.

-A two-sided test with zcrit = -1.645 and 1.645.

-n 1 = n 1999 = 334

-n 2 = n 2009 = 843

-p ^ 1 = p ^ b i n g e 1999 = 0.422

-p ^ 2 = p ^ b i n g e 2009 = 0.212

A) Calculate the appropriate test statistic. What is the standard error?

B) What is the test statistic value?

C) Calculate the corresponding p-value from the appropriate table.

D) Construct a 90% confidence interval around the difference-in-proportions estimate. Lower bound and upper bound values?