## I. Given the sample set below.(Round your answers to two decimal places.)

Question I. Given the sample set below.(Round your answers to two decimal places.) 6 18 11 19 40 16 18 21 11 23 6 21 18 31 10 20 31 27 18 24 25 (9 pts) a. Calculate the sample mean ¯x, sample standard deviation s and simple variance s 2 . (2 pts) b. Find the mode of the sample set. (5 pts) c. Find the five-number-summary. (9 pts) d. Determine if there are any outliers. Why?

## III. A friend of mine is giving a dinner party. His current wine supply

Question III. A friend of mine is giving a dinner party. His current wine supply includes 6 bottles of zinfandel, 8 of merlot, and 10 of cabernet (he only drinks red wine), all from different wineries. (5 pts) (a). If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to? (5 pts) (b). If 6 bottles of wine are to be randomly selected from the 24 for serving, how many ways are there ? (5 pts) (c). If 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? (5 pts) (d). If 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (5 pts) (e). If 6 bottles are randomly selected, what is the probability that all of them are the same variety?

## Samples of “lean” hamburger were selected from two different outlets

Question Samples of “lean” hamburger were selected from two different outlets of a large supermarket to measure the percentage of fat present in the meat, with the following summary data. Outlet 1 Outlet 2. n 11 14 mean 10.3 10.7 variance 2.6 2.2 What are the degrees of freedom for the pooled estimate in the question above? A. 24 B. 23 C. 22 D. 12 E. 143

## Case Problem –

The National Public Health Institute of Uganda is a consulting institution of health professionals whose wide

Question Case Problem –

The National Public Health Institute of Uganda is a consulting institution of health professionals whose wide knowledge and experiences in various disciplines of healthcare have contributed positively to the competencies of fellow health professionals. The institute is committed to strengthening Ugandan health system through partnerships and sound healthcare interventions. The organisation has a mission to provide quality and outcome-based professional support services to public health sector and communities with the vision on science-based public health interventions for better health outcomes. The Uganda health is concerned about the shortage of nurses the health care profession is projecting for the future. To learn the current degree of job satisfaction among nurses, the association has sponsored a study of hospital nurses throughout the country. As part of this study, a sample of 50 nurses were asked to indicate their degree of satisfaction in their work, their pay, and their opportunities for promotion. Each of the three aspects of satisfaction was measured on a scale from 0 to 100, with larger values indicating higher degrees of satisfaction. The data were broken down by the types of hospitals employing the nurses and are presented in the table below. The types of hospitals considered were private, Veterans Administration, and University. Use methods of descriptive statistics to summarize the data. Present the summaries that will be beneficial in communicating the results to others. Discuss your findings. Specifically, comment on the following questions: QuestionWhat can be learned about the types of hospitals? Does any particular type of hospital seem to have better levels of job satisfaction than the other types? (Construct a frequency distribution for each hospital type using eight number of classes. In the table, include the following columns: class, frequency, midpoints, relative frequencies, and cumulative frequencies. Construct a frequency histogram for each type of hospital and comment. Estimate the mean and standard deviation hospital satisfaction score) Question On the basis of descriptive measures of variability, what measure of job satisfaction appears to generate the greatest difference of opinion among the nurses? Explain. Question On the basis of the entire data set and the three job satisfaction variables, what aspect of the job is most satisfying for the nurses? What appears to be the least satisfying? In what area(s), if any, do you feel improvements should be made? Discuss. (Hint: compute the mean, median, mode for each aspect and five-number summary; and construct the Box-and-Whisker Plot)

## In a statistical test for the equality of a mean, such as H0: mean

Question In a statistical test for the equality of a mean, such as H0: mean = 10, if alpha = 0.01, and the null hypothesis is rejected, which of the following is true? A. 1% of the time we will conclude that there is a difference when there is a real difference B. 1% of the time we will conclude that there is a difference when there is no real difference C. 99% of the time the null hypothesis will be correct D. 99% of the time we will make an incorrect inference E. 1% of the time we will make an incorrect inference no matter the outcome of such a test

## 1. Ultrasound was used to gather the accompanying corrosion data on the thickness of the oor plate of

Question 1. Ultrasound was used to gather the accompanying corrosion data on the thickness of the oor plate of an aboveground tank used to store crude oil. Each observation in the following sample is the largestpit depth in the plate, expressed in milli-in.40, 52, 55, 60, 70, 75, 85, 85, 90, 90, 92, 94, 94, 95, 98, 100, 115, 125, 125a) Find the 5-number summary of the above sample [5]b) Draw a rough boxplot for the data. Is the data symmetric or skewed? give a very short explana-tion [5]

## The makers of a smartphone have received complaints that the face

Question The makers of a smartphone have received complaints that the face recognition tool often doesn’t work, or takes multiple attempts to finally unlock the phone. They’ve upgraded to a new version and are claiming the tool has improved. To test the claim, a critic takes a random sample of 80 users of the new version (Group 1) and 75 users of the old version (Group 2). He finds that the face recognition tool works on the first try 75% of the time in the new version and 60% of the time in the old version. Can it be concluded that the new version is performing better? Test at α=0.10.Hypotheses:H0: p1 = p2H1: p1

## Let X and Y be continuous random variables. The joint probability density function of X and Y is

Question Let X and Y be continuous random variables. The joint probability density function of X and Y is f(x, y) ={ 12x^3y ;0 < y < x < 1; 0 ;otherwise }1. Find the margin probability density function fX(x) of X.2. Find the conditional probability density function fX|Y (x|y) of X given Y.