Modern medical practice tells us not to encourage babies to become too fat. Is there a positive correlation between the weight x of a 1-year old baby and the weight y of the mature adult (30 years old)? A random sample of medical files produced the following information for 14 females.

In this setting we have Σx = 297, Σy = 1770, Σx² = 6431, Σy² = 224,880, and Σxy = 37,734.

(a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your answers for least-squares estimates to four decimal places.)

(b) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.)

What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)

(c) Test the claim that the population correlation coefficient ρ is positive at the 1% level of significance. (Round your test statistic to three decimal places.)

t =

Find the p value =

(d) If a female baby weighs 15 pounds at 1 year, what do you predict she will weigh at 30 years of age? (Round your answer to two decimal places.)

(e) Find S_e. (Round your answer to two decimal places.)

(f) Find a 95% confidence interval for weight at age 30 of a female who weighed 15 pounds at 1 year of age. (Round your answers to two decimal places.)

(g) Test the claim that the slope β of the population least-squares line is positive at the 1% level of significance. (Round your test statistic to three decimal places.)

t =

Find the P value =

(h) Find an 80% confidence interval for β and interpret its meaning. (Round your answers to three decimal places.)

uppose that the longevity of a light bulb is exponential with a mean lifetime of eight years. (a) Find the probability that a light bulb lasts less than one year. (Round your answer to four decimal places.) (b) Find the probability that a light bulb lasts between six and ten years. (Round your answer to four decimal places.) (c) Seventy percent of all light bulbs last at least how long? (Round your answer to two decimal places.) yr (d) A company decides to offer a warranty to give refunds to light bulbs whose lifetime is among the lowest three percent of all bulbs. To the nearest month, what should be the cutoff lifetime for the warranty to take place? (Round your answer up to the next month.) months (e) If a light bulb has lasted seven years, what is the probability that it fails within the eighth year. (Round your answer to four decimal places.)

Two nonprofits are interested in sharing fundraising lists and campaigns as they think their donors share common interests. Implicit in that assumption is they are related variables. You collect data below for thirteen donors and want to test if there is a relationship between donations (in dollars) (data is collected below)

Charity A:  

50 70 60 30 30 60 100 20 40 60 30 80 60

Charity B:

60 45 65 50 30 30 90 40 50 70 40 55 40

a.) State the null both formally and in lay terms
b) Calculate r and the regression line (y = a + bx) and reject/accept at a=.05. What is the regression line please state it?

c) Explain your findings in lay terms using r-square, r, b as appropriate

d) Calculate a 95% confidence interval for the slope if it is necessary if it is not please explain. Provide the formal interval and explain in layterms.

Consider a senior Statistics concentrate with a packed extracurricular schedule, taking five classes, and writing a thesis. Each time she takes a test, she either scores very well (at least two standard deviations above the mean) or does not. Her performance on any given test depends on whether she is operating on a reasonable amount of sleep the night before (more than 7 hours), relatively little sleep (between 4 - 7 hours, inclusive), or practically no sleep (less than 4 hours).

When she has had practically no sleep, she scores very well about 30% of the time. When she has had relatively little sleep, she scores very well 40% of the time. When she has had a reasonable amount of sleep, she scores very well 42% of the time. Over the course of a semester, she has a reasonable amount of sleep 50% of nights, and practically no sleep 30% of nights.
a) What is her overall probability of scoring very well on a test?
b) What is the probability she had practically no sleep the night before an test where she scored very well?
c) Suppose that one day she has three tests scheduled. What is the probability that she scores very well on exactly two of the tests, under the assumption that her performance on each test is independent of her performance on another test?
d) What is the probability that she had practically no sleep the night prior to a day when she scored very well on exactly two out of three tests?

Renee is studying the effect of positive reinforcement for her psychology She gets 16 pigeons. These pigeons are from eight egg clutches with two pigeons from each clutch. Renee matches/pairs each pigeon in Reinforcement Schedule A with its clutchmate in Reinforcement Schedule B. After training the pigeons, she measures the number of correct responses by each in 10 trials. Using a two-tailed test and , α =0.05, use the data below to determine whether or not there is a difference between the two schedules.

1. What type of t-test should you use?
2. What are your degrees of freedom?
3. What is the appropriate ?  t-crit
4. Calculate t-obt
5. Report your results

A newly built old age home has 50 townhouses. Residents may only plant clivias, rose bushes and lavenders in their gardens. Of the 50 gardens 20 grow clivias, 22 grow roses, and 24 grow lavenders. (Residents do not necessarily plant only one of the kinds of plants.) Furthermore, some gardens grow the following: 6 grow clivias and rose bushes 8 grow clivias and lavenders, (Residents do not necessarily plant only two of the kinds of plants.) 4 grow clivias, rose bushes and lavenders. How many gardens have rose bushes and lavenders, but no clivias?

Think of a password 8 character long which uses at last one lower-case letter, one capital letter, and one number, but uses none more than once.
What's your password?

How many possible permutations are there for an 8 character password which meets those criteria?

How many fewer combinations without regard to order are there for an 8 character password which meets those requirements.

How would you calculate how many permutations there are for an 8 to 12 character password which meets those criteria?

4-8

Diego Company manufactures one product that is sold for $78 per unit in two geographic regions—the East and West regions. The following information pertains to the company’s first year of operations in which it produced 49,000 units and sold 44,000 units.

The company sold 32,000 units in the East region and 12,000 units in the West region. It determined that $230,000 of its fixed selling and administrative expense is traceable to the West region, $180,000 is traceable to the East region, and the remaining $100,000 is a common fixed expense. The company will continue to incur the total amount of its fixed manufacturing overhead costs as long as it continues to produce any amount of its only product.

What is the company’s break-even point in unit sales?

1. Insomnia has become an epidemic in the United States. Much research has been done in the development of new pharmaceuticals to aide those who suffer from insomnia. Alternatives to the pharmaceuticals are being sought by sufferers. A new relaxation technique has been tested to see if it is effective in treating the disorder. Sixty insomnia sufferers between the ages of 18 to 40 with no underlying health conditions volunteered to participate in a clinical trial. They were randomly assigned to either receive the relaxation treatment or a proven pharmaceutical treatment. Thirty were assigned to each group. The amount of time it took each of them to fall asleep was measured and recorded. The data is shown below. Run an independent samples t-test to determine if the relaxation treatment is more effective than the pharmaceutical treatment at a level of significance of 0.05. Report the test statistic using correct APA formatting and interpret the results.