Researchers at the University of South Florida conducted a study of drug usage of U.S. physicians. The anonymous survey of 5,430 randomly selected physicians revealed that 429 experienced substance abuse or drug dependency in their lifetime. Test the hypothesis that more than 5% of US. physicians have used or depended on drugs in their lifetime at a 0.05. State the null and alternative hypothesis. State your conclusion for your hypothesis test. Give the 95% Confidence Interval. Give a conclusion for the confidence interval test.

Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular breakfast place is shown in Table. Conduct a test for homogeneity at a 5% level of significance. . French Toast Pancakes Waffles Omelettes
Men 47 35 28 53
Women 65 59 55 60

A geologist collects hand-specimen sized pieces of limestone from a particular area. A qualitative assessment of both texture and color is made with thefollowing results. Is there evidence of association between color and texture for these limestones? Explain your answer. Texture /Color Light Medium Dark
Fine 4 20 8
Medium 5 23 12
Coarse 21 23 4

At a school pep rally, a group of sophomore students organized a free raffle for prizes. They claim that they put the names of all of the students in the school in the basket and that they randomly drew 36 names out of this basket. Of the prize winners, 6 were freshmen, 14 were sophomores, 9 were juniors, and 7 were seniors. The results do not seem that random to you. You think it is a little fishy that sophomores organized the raffle and also won the most prizes. Your school is composed of 30% freshmen, 25% sophomores, 25% juniors, and 20% seniors. a. What are the expected frequencies of winners from each class? b. Conduct a significance test to determine whether the winners of the prizes were distributed throughout the classes as would be expected based on the percentage of students in each group. Report your Chi Square and p values. c. What do you conclude?

The fill volume of an automated filling machine used for filling cans of carbonated beverage is normally distributed with a mean of 12.4 grams and a standard deviation of 0.1 grams. i) What is the probability a fill volume is less than 12 grams? ii) If all cans less than 12.1 grams or greater than 12.6 grams are scrapped, what proportion of cans is scrapped? iii) Determine specifications that are symmetric about the mean that include 99% of cans.

The thickness of a plastic film (in mm) on a substrate material is thought to be influenced by the temperature at which the coating is applied. A completely randomized experiment is carried out. Eleven substrates are coated at 125$^o$C resulting in a sample mean thickness of $\overline{x}_1=103.5$ mm and a sample standard deviation of $s_1=10.2$ mm. Another 13 substrates are coated at 150$^o$C for which $\overline{x}_2 =99.7$ mm and $s_2 = 20.1$ mm are observed. It was originally suspected that raising the process temperature would reduce mean coating thickness. i) Calculate a 95% confidence interval for the population mean for substrate one. ii) Calculate a 95% confidence interval for the mean difference in the thickness of the two substrates, is the original claim true (assume the variances are statistically equivalent). Interpret the result.

A company has recently started building a new plant. Letting A represent the number of months to complete the project, the probability distribution of A is: $P(A)=\frac{A}{22}, A = 4,5,6,7.$ i) Show that P(A) is a probability function. ii) What is the probability that the plant will be completed in at most 6 months? iii) What is the probability it will be completed in at least 5 and not more than 6 months?

The following data represents viscosity measurements from a batch chemical process. The data is assumed to be normally distributed. The batches are checked for conformance to specification. Batches whose viscosity lies between 84 and 96 are acceptable. A random sample of 89 batches are checked. Viscosity Measure <80 80-84 84-88 88-92 92-96 96-100 >100
Frequency 0 7 21 33 23 5 0 i) Calculate the mean, standard deviation, standard error of the mean and coefficient of variation of the data. ii) Interpret the mean and standard deviation in the context of the problem.

A crossover study was conducted to investigate whether oat bran cereal helps to lower serum cholesterol levels in hypercholesterolemic males. Fourteen such individuals were randomly placed on a diet that included either oat bran or corn flakes; after two weeks, their low density lipoprotein (LDL) cholesterol levels were recorded. Each man was then switched to the alternative diet. After a second two week period, the LDL cholesterol level of each individual was again recorded. The data from this study are shown below. Subject LDL (mmol/l) Corn Flakes LDL (mmol/l) Oat Bran
1 4.61 3.84
2 6.42 5.57
3 5.4 5.85
4 4.54 4.8
5 3.98 3.68
6 3.82 2.96
7 5.01 4.41
8 4.34 3.72
9 3.8 3.49
10 4.56 3.84
11 5.35 5.26
12 3.89 3.73
13 2.25 1.84
14 4.24 4.14 a) Are the two samples of data paired or independent? b) What are the appropriate Null and alternative hypothesis for a two sided test? c) Conduct the test

Suppose that you are interested whether exposure to the organochlorine DDT which has been used extensively as an insecticide for many years, is associated with breast cancer in women. As part of the study that investigated this issue, blood was drawn from a sample of women diagnosed with breast cancer over a six year period and from a sample of healthy controls subject matched to the cancer patients on age, menopausal status, and date of blood donation. Each woman's blood level of DDE-an important by product of DDT in the human body was measured, and the difference in levels for each patient and her matched control calculated. A sample of 171 such differences has mean $\overline{d}=2.7$ ng/ml and standard deviation $s_d =15.9$ ng/ml a) Test the null hypothesis that the mean blood levels of DDE are identical for women with breast cancer and for healthy control subjects. What do you conclude? b) Would you expect a 95% confidence interval for the true difference in population mean DDE lev