1. Assume the monthly price change per share of Tencent follows a normal distribution with μ=2.8 and ?=15.
   1. (5) If you buy one share of Tencent and hold for one month, what is the chance you will lose money?
   2. (5) Assume that the performance of stock price is independent across different months. If you hold the stock for 12 months, what is the chance that you will only lose in 2 months?
   3. (5) Continue from (b). What is the chance that you don’t lose until 12^th month?
   4. (5) If you buy and hold 1 share of Tencent for one year, what is the chance you will lose money at the end of the year?

A machine that produces a special type of transistor (a component of computers) has a 10% defect rate. The production is considered a random process where each transistor is independent of the others. What is the probability that the 5th transistor produced is the first with a defect? Which distribution would you use here and why?

1. The mean starting salary for college graduates in spring of 2018 was $43,200. Assume that the distribution of starting salaries follows the normal distribution with a standard deviation of $3500. What percent of the graduates have starting salaries:

A.) Less than $38,000?

B.) More than $45,000?

C.) Between $38,000 and $45,000?

A random sample of 100 daily stock returns was taken. The average return in the sample appeared to be 4.81%. The population standard deviation is not known, but the sample standard deviation is known to be 0.9%.

a.  Calculate a 95% confidence interval for the average stock return

b. How big the sample size be for the margin of error of 0.1% at the confidence level 95%?

c. A fund manager claims that the average stock return is higher than 4.81%. Test the fund manager’s claim with the 5% level of significance.

Prevalence of autism in children of Somali origin living in Stockholm: brief report of an at-risk population. Based on a study by Barnevik-Olsson M, Gillberg C, Fernell E: This work was a follow-up study (birth years 1999-2003) of the prevalence of autism in children of Somali background living in the county of Stockholm, Sweden. In a previous study (birth years 1988-98), the prevalence of autism associated with learning disability was found to be three to four times higher among Somali children compared with other ethnicities in Stockholm. We examined all records of children of Somali background, born from 1999 to 2003, registered at the centre for schoolchildren with autism and learning disability. The census day was 31 December 2009. The sample prevalence of autism and PDDNOS (with learning disability) was 0.98% (18/1836) in the Somali group compared with the 0.21% in the group of children of non-Somali origin.

• Do the data suggest a higher prevalence of autism in children of Somali background? (source: PMID:20964674 PubMed).
• In UK the prevalence of autism is 1%. Do the Swedish data suggest a higher autism prevalence in children of Somali background than UK the prevalence?

Would frequent brief project evaluations be best, or would less frequent major evaluations be preferred? Explain your answer.

In this study patients were recruited from 3 different clinical sites. Use the following data to test if there is a difference in the proportions of hypertensive patients across clinical sites.

(old fashioned step by step process, Excel is okay but no electronic computing like ANOVA, please)

Let X1, . . . , Xn ∼ iid Unif(0, θ). (a) Is this family MLR in Y = X(n)? (b) Find the UMP size-α test for H0 : θ ≤ θ0 vs H1 : θ > θ0. (c) Find the UMP size-α test for H0 : θ ≥ θ0 vs H1 : θ < θ0. (d) Letting R1 be the rejection region for the test in part (b) and R2 be the rejection region for the test in part (c). Consider the test for the hypotheses H0 : θ = θ0 vs H1 : θ 6= θ0 determined by the rejection region R = R1 ∪ R2. That is, we reject H0 if the data is in either R1 or R2. Find the power function of this test and comment on the size.

1. A researcher is interested in testing two different dosages of a new sleeping medication in a phase II clinical trial against a control group receiving a placebo. Suppose the following table observes the hours of sleep reported the preceding evening for subjects randomly assigned to each of the three groups. α = .05 Dosage One 8.5, 7.9, 8.6, 8.4, 7.6, 9.1. Dosage Two- 8.1, 7.9 , 7.9, 7.6, 7.4. Control Group- 5.2, 5.6, 5.7, 5.9, 6.2, 6.4, 6.1.

A) Calculate the MSB and MSW for a one-way analysis of variance procedure. B) Using the information above, calculate an F statistic, and provide an interpretation of your p-value. (Continue as though all assumptions for ANOVA are met). How would you solve this without using excel?

1. A survey about same-sex marriage used a random sample with 1200 adults. The results showed that 30% favored legal marriage, 32% favored civil unions, and 38% favored no legal recognition. Computer the right boundary at the 91% C.L. for the proportion of adults who favor the “legal marriage” position.

2. A survey about same-sex marriage used a random sample with 1200 adults. The results showed that 30% favored legal marriage, 32% favored civil unions, and 38% favored no legal recognition. Computer the right boundary at the 94% C.L. for the proportion of adults who favor the “civil union” position.

3. A survey about same-sex marriage used a random sample with 1200 adults. The results showed that 30% favored legal marriage, 32% favored civil unions, and 38% favored no legal recognition. Computer the right boundary at the 97% C.L. for the proportion of adults who favor the “no legal recognition” position.

Because of the rising costs of industrial accidents, many chemical, mining, and manufacturing firms have instituted safety courses. Employees are encouraged to take these courses designed to heighten safety awareness among them. A company is trying to decide which one of two courses to institute. To help make a decision, eight employees take course 1, and another group of eight take course 2. Each employee takes a test, which is graded out of a possible 25 marks. The safety test results of these employees are shown below. Assume that the scores are normally distributed.

Course 1   Course 2
Sample Mean   12.3750   19.1250
Sample SD   2.7222   2.9970

SD=Standard Deviation

Do these data provide enough evidence at the 5% level of significance to infer that the marks from course 1 are lower than those of course 2?

The following data were collected in an experiment designed to investigate the impact of different positions of the mother during ultrasound on fetal heart rate. Fetal heart rate is measured by ultrasound in beats per minute. The study includes 20 women who are assigned to one position and have the fetal heart rate measured in that position. Each woman is between 28-32 weeks gestation. The data are shown below.

Is there a significant difference in mean fetal heart rates by position? Run the test at a 5% level of significance.

(step by step needs to be shown, no SSPS or ANOVA calculations: old fashioned way only).

26 randomly selected students were asked the number of movies they watched the previous week. The results are as follows:

Round all your answers to one decimal place.

The mean is:

The median is:

The sample standard deviation is:

The first quartile is:

The third quartile is:

What percent of the respondents watched at least 4 movies the previous week? ______%

74% of all respondents watched fewer than how many movies the previous week?

Consider the following linear programming problem:

                  Maximize Profit    30X + 50Y

                  Subject to              4X +   5Y = 40,000

                                                               X ≥   3,000

                                                               Y ≥   4,000

                                                    X ≥ 0 and Y ≥ 0

1. Use a graph to show each constraint and to identify feasible region.
2. Identify the optimal solution point on your graph. What are the values of X and Y at the optimal solution?
3. From your graph, what is the optimal value of the objective function?