Cloud seeding has been studied for many decades as a weather modification procedure (for an interesting study of this subject, see the article in Technometrics, "A Bayesian Analysis of a Multiplicative Treatment Effect in Weather Modification", Vol. 17, pp. 161–166). The rainfall in acre-feet from 20 clouds that were selected at random and seeded with silver nitrate follows: 19.0, 31.7, 20.8, 28.1, 23.3, 19.8, 32.8, 24.4, 22.2, 28.9, 32.9, 28.1, 26.0, 25.7, 27.9, 22.8, 30.2, 35.8, 27.7, 32.6

(a) Can you support a claim that mean rainfall from seeded clouds exceeds 26.0 acre-feet? Use α=0.01.

(b) Compute the power of the test if the true mean rainfall is 28.0 acre-feet.

(c) What sample size would be required to detect a true mean rainfall of 28.5 acre-feet if we wanted the power of the test to be at least 0.9?

In a survey, 29 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $33 and standard deviation of $15. Use the theory-based inference applet to find the confidence interval at a 99% confidence level. Give your answers to one decimal place.

• We are 99% confident that the average (mean) amount that people spent on their child's last birthday gift, μμ, was between  dollars and  dollars.
  
• The sample statistic is  dollars.
  
• The margin of error is  dollars.
• The confidence interval can be written as
  dollars ±±  dollars.

1. The size of the left upper chamber of the heart is one measure of cardiovascular health. When the upper left chamber is enlarged, the risk of heart problems is increased. The paper “Left atrial size increases with body mass index in children” (International Journal of Cardiology [2009]: 1–7) described a study in which the left atrial size was measured for a large number of children age 5 to 15 years. Based on this data, the authors concluded that for healthy children, left atrial diameters were approximately normally distributed with a mean of 26.4 mm and a standard deviation of 4.2 mm.

a. About what proportion of healthy children have left atrial diameters greater than 32 mm?

b. About what proportion of healthy children have left atrial diameters between 25 mm and 30 mm?

c. Children in the top 10% of left atrial diameters are at risk of heart problems. What is the left atrial diameter value (the original x value) describing the upper 10% of extreme left atrial diameters? (Hint: What percentile is this, draw a figure).

15.9 For a sample of 8 employees, a personnel director has collected the following data on ownership of company stock versus years with the firm.

x = 5 Years

    6
   12
   14
    6
    9
   13
   15
    9

y = 5 Shares

    300
    408
    560
    252
    288
    650
    630
    522

1. Determine the least-squares regression line and interpret its slope.

2. For an employee who has been with the firm 10 years, what is the predicted number of shares of stock owned?

For the data in Exercise 15.9, find the standard error of estimate, then construct the 95% prediction interval for the amount of stock owned by an individual employee who has been with the firm for 5 years.

Please construct the

1. The 95% confidence interval for x=10 for the average number of shares own for all the employees have 10 years of service with firm. 4 points

2. The 95% prediction interval for one employee who has 10 years service with the firm.4 points

Use the following multiple regression table to answer the following questions:

1. What is the Y-intercept for the output of the data?

2. What is the R^2 of the data?

3. What is the adjusted R^2?

4. What is the high temperature coefficient of the output?

5. What is the price coefficient?

6. What is the Day Coefficient of the output, if the day is a weekday?

7. Using the data output, Calculate demand for burritos on a day that is 75 degrees, the price is $1.10...and it is a weekend.

8. Using the data output, Calculate demand for burritos on a day that is 75 degrees, the price is $1.10...and it is a weekday.

9. Using the data output, Calculate demand for burritos on a day that is 85 degrees, the price is $1.05...and it is a weekend.

10. Using the data output, Calculate demand for burritos on a day that is 85 degrees, the price is $1.05...and it is a weekday.

Q2. Distance (000, miles) traveled by a truck in a year is distributed normally with μ = 50.0 and σ = 12.0.

       Find

a. the proportion of trucks are expected to travel from 34.0 to 59 (000, miles)? (0.6816)

b. the probability that a randomly selected truck travels from 34.0 to 38.0 (000, miles)? (0.0669)

c. the %age of trucks that are expected to travel either below 30.0 or above 59.0 (000 miles) ? (27.41)

d. how many of the 1000 trucks in the fleet are expected to travel from 30.0 to 59.0 (000 miles)? (726)

e. how many miles will be traveled by at least 80% of the trucks? (40, 000 miles)

Q1. From a reputed store’s record it was found that weight of sugar bags sold by it is normally distributed

       with mean 1.0 lb. and standard deviation of 40 g.

a. What is the probability/chances/likelihood that

i. a bag selected randomly will be lighter than 400 g (0.0901)

ii. a bag selected randomly will be heavier than 600 g (0.00013)

         iii. the weight will be more than 463.5 g. if a customer bought one bag,? (0.4013)

       b What proportion of customers are expected to buy heavier than 470 g,

           if one customer can buy one bag? (0.3409)

       c. How many bags are expected to be heavier than 470 g,

          if it has a stock of 1000 bags in the store? (341 bags)

       d. What proportion of bags will be heavier than 1.0 lb.? (0.5)

       e. A random sample of 64 bags was selected.

         i. mean weight of the sample will be more than 461.8 g.? (0.0505)

         ii. the mean weight will between 443.8 g. to 463.4 g.(0.95)

       f. From what weight

           i. 25% bags will be heavier? (480.6 g.)    ii. 25% bags will be lighter? (426.6 g.)

Suppose you have two groups, with Group 1's sample size being 76 and Group 2's sample size being 68. The average of the first group is 31.85 and a sample standard deviation of 10.44. The average of the second group is 29.16 and a sample standard deviation of 11.1. Can you reject the null that there is no difference between the two groups at the 99% significance level?

H0: μ_1,0 - μ_2,0 = 0

HA: μ_1,0 - μ_2,0 ≠ 0

What is the Standard Error for this situation? SE =  

What is the t-score for this situation? t =

Question 1:

A binomial distribution has p = 0.21 and n = 94. Use the normal approximation to the binomial distribution to answer parts (a) through (d) below. Round to four decimal places as needed.)

a. What are the mean and standard deviation for this distribution?

b. What is the probability of exactly 15 successes?

c. What is the probability of 13 to 21 successes?

d. What is the probability of 9 to 17 successes?

Question 2:

The average number of miles driven on a full tank of gas in a certain model car before its low-fuel light comes on is 331. Assume this mileage follows the normal distribution with a standard deviation of 44 miles. Complete parts a through d below. (Round to four decimal places as needed.)

1. What is the probability that, before the low-fuel light comes on, the car will travel less than 361 miles on the next tank of gas?
2. What is the probability that, before the low-fuel light comes on, the car will travel more than 280 miles on the next tank of gas?
3. What is the probability that, before the low-fuel light comes on, the car will travel between 301 and 321 miles on the next tank of gas?
4. What is the probability that, before the low-fuel light comes on, the car will travel exactly 353 miles on the next tank of gas?

A consumer preference study compares the effects of three different bottle designs (A, B, and C) on sales of a popular fabric softener. A completely randomized design is employed. Specifically, 15 supermarkets of equal sales potential are selected, and 5 of these supermarkets are randomly assigned to each bottle design. The number of bottles sold in 24 hours at each supermarket is recorded. The data obtained are displayed in the following table.

The Excel output of a one-way ANOVA of the Bottle Design Study Data is shown below.

(a) Test the null hypothesis that μ_A, μ_B, and μ_C are equal by setting α = .05. Based on this test, can we conclude that bottle designs A, B, and C have different effects on mean daily sales? (Round your answers to 2 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

(Click to select)Do not rejectReject H₀: bottle design (Click to select)doesdoes not have an impact on sales.

(b) Consider the pairwise differences μ_B – μ_A, μ_C – μ_A , and μ_C – μ_B. Find a point estimate of and a Tukey simultaneous 95 percent confidence interval for each pairwise difference. Interpret the results in practical terms. Which bottle design maximizes mean daily sales? (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

Bottle design (Click to select)CBA maximizes sales.

(c) Find a 95 percent confidence interval for each of the treatment means μ_A, μ_B, and μ_C. Interpret these intervals. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

You have collected data for 104 countries to address the difficult questions of the determinants for differences in the standard of living among the countries of the world. Your model has the relative personal income (RelPersInc) determined by the saving rate (SK) and population growth rate (n). To test the predictions of this growth model, you run the following regression:

= 0.339 – 12.894 × n + 1.397 × SK,      R2=0.621

                  (0.068) (3.177)     (0.229)

Numbers in parentheses are the standard errors.

1. Calculate the t-statistics and test whether or not each of the population parameters are significantly different from zero.

2. Calculate the overall F-statistic for the regression. Test the null hypothesis that that all the slope coefficients are equal to zero at the 5% level.

You remember that human capital in addition to physical capital also plays a role in determining the standard of living of a country. You therefore collect additional data on the average educational attainment and add this variable (Educ) to the above regression. This results in the modified regression output:

= 0.046 – 5.869 × n + 0.738 × SK + 0.055 × Educ,    R2=0.775,

                      (0.079)   (2.238)      (0.294)           (0.010)

3. How has the inclusion of Educ affected your previous results?

4. Perform a test to find out if it is worth keeping Educ in the model at the 5% level.

global research study found that the majority of​ today's working women would prefer a better​ work-life balance to an increased salary. One of the most important contributors to​ work-life balance identified by the survey was​ "flexibility," with 45​% of women saying that having a flexible work schedule is either very important or extremely important to their career success. Suppose you select a sample of 100 working women.

The probability that in the sample fewer than 53​% say that having a flexible work schedule is either very important or extremely important to their career success is ___.

The probability that in the sample between 41​% and 53​% say that having a flexible work schedule is either very important or extremely important to their career success is ___.

The probability that in the sample more than 47​% say that having a flexible work schedule is either very important or extremely important to their career success is ___.

Corporate advertising tries to enhance the image of the corporation. A study compared two ads from two sources, the Wall Street Journal and the National Enquirer. Subjects were asked to pretend that their company was considering a major investment in Performax, the fictitious sportswear firm in the ads. Each subject was asked to respond to the question "How trustworthy was the source in the sportswear company ad for Performax?" on a 7-point scale. Higher values indicated more trustworthiness. Here is a summary of the results.

Find the two-sample pooled t statistic. Then formulate the problem as an ANOVA and report the results of this analysis. Verify that F = t ².

______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Is the following statement true or false? Give your answer and briefly explain it.

"A research study’s sample can be another research study’s population."