From a sample of 23 graduate students, the mean number of months of work experience prior to entering an MBA program was 33.24. the national standard deviation is known to be 19 months. what is a 99% confidence interval for the population mean?

This question is to give you a feel for the actual calculations involved with OLS regressions. In this case, the independent variable is time (t). We will talk more about adding time as a variable later. For now, just treat it like any other independent variable x. You should do the calculations manually without a computer. It is very important that you show your work as answers will vary a bit due to rounding errors so I need to know that you followed the correct methodology. I recommend not trying to type up your answers as typing this many numbers will likely involve at least some typos. Consider the following data (continued on next page):

(e) Find the F-statistic. Is the equation significant at the 1% level? Make sure you state the null and alternative hypotheses. Use the p-value approach.

(f) Find the 95% prediction interval for when t = 5.

(g) There are two ways of calculating SSR (a direct and an indirect way). You would have used one method for previous parts of this question. Now, use the method you did not previously use.

Show your progress and I'll rate your answer good! (It's in Excel btw) Thanks:)

A population has a mean of 300 and a standard deviation of 90. Suppose a sample of size 125 is selected and  is used to estimate . Use z-table.

1. What is the probability that the sample mean will be within +/- 7 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.)
   
2. What is the probability that the sample mean will be within +/- 13 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.)

Does crime pay? The FBI Standard Survey of Crimes showed that for about 80% of all property crimes (burglary, larceny, car theft, etc.), the criminals are never found and the case is never solved†. Suppose a neighborhood district in a large city suffers repeated property crimes, not always perpetrated by the same criminals. The police are investigating three property crime cases in this district.

(a) What is the probability that none of the crimes will ever be solved? (Round your answer to three decimal places.)


(b) What is the probability that at least one crime will be solved? (Round your answer to three decimal places.)


(c) What is the expected number of crimes that will be solved? (Round your answer to two decimal places.)
crimes

What is the standard deviation? (Round your answer to two decimal places.)
crimes

(d) How many property crimes n must the police investigate before they can be at least 90% sure of solving one or more cases?
n = crimes

Psychologists are interested in finding out what proportion of men and women have ended a budding relationship because a kiss did not go well. A survey was administered to a random sample of adults and asked each individual to disclose whether they ended a budding relationship because a kiss did not go well. The results of the survey are summarized in the table.

a) Identify whether the sampling method used in this study is independent or dependent. Explain.

b) Obtain a point estimate for the proportion of men who have ended a budding relationship because a kiss did not go well. Obtain a point estimate for the proportion of women who have ended a budding relationship because a kiss did not go well.

c) Does the data suggest that a lower proportion of men have ended a budding relationship because a kiss did not go well than women at the ? = 0.05 level of significance? Use the critical value method. (Show all six steps for hypothesis testing.)

d) Estimate the difference in proportion of men and women who have ended a budding relationship because a kiss did not go well with 90% confidence. Does the sample evidence suggest there is a difference between the two population proportions? If so, interpret and describe the difference by identifying which group has a lower proportion.

In estimating the average price of a gallon of gasoline in a region we plan to select a random sample (independent and identically distributed) of size 10. Let X1, X2, ... , X10 denote the selected sample. The two estimators for estimating the average price, μ , are:

U1 = (X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 +X9 + X10)/10

U2 = (X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 )/8 + X1 - X2 .

a. which of the above estimators are unbiased? Fully justify your answer.

b. Using the mean square error criterion, determine which estimator is better.

The Kingdom of Saudi Arabia is blessed with a wealth of energy resources such as the large oil
reserves that reach 266,455 M barrels. However, with the increasing population that is currently
growing at a rate of 2.54%, the electricity demand is expected to double in the next ten years.
Looking at the current power generation systems, one can recognize that it is dominated by steam
power plants and desalination cogeneration plants which produce 55,718 MW and 36,800,705
MWh, respectively.
In this context, you are requested to write a report on the electricity generation in Saudi Arabia.
Your report should include the following:
1- A detailed description and analysis of simple Rankine steam power plant. Writing the mass
balance (MBE), the energy balance (EBE), and the entropy balance equations for each
component. Plot the T-s and flow diagrams.
2- Write a brief description of an actual steam power plant that is currently in operation in
Saudi Arabia (about one page). Provide references for your information.
3- Write about one page on the advantages and disadvantages of oil-based power plants.
4- One of the disadvantages of oil-based power plants is the CO2 and air pollutant produced
by these plants. What are the possible solutions to this problem?
5- As part of the promising Saudi Vision 2030, the electricity generation will be less
dependent on oil. Describe some of the renewable energy options that will be introduced
through the Saudi Vision 2030. Refer to some projects and provide references for your
information.

Problem 1: Remember when I asked you for your age on the first day of class? Well here is a larger subset of the data that I collected: 18 18 18 18 19 19 19 19 20 20 20 20 21 21 21 21 21 21 21 22 22 22 22 23 24 26 26 28 32 33 46 a)Someone once told me that the average age of students at PSU was 26 years old. Identify the null and alternative hypotheses to test if our class has a significantly different mean age. b)In class, we talked about how we need to know three things to test a hypothesis. Discuss them and explain what they are in the context of this problem. c)Find the critical value associated with this test (α=.05) and use it to find a 95% confidence interval for the true mean student age. d)Calculate the test statistic and associated p-value. e)In class we talked about three different ways come to a decision about whether to reject the null. Describe and carry out all these three methods using your answers to parts c and d. (Remember that they should all lead to the same decision.) f)State your decision and formulate a conclusion in terms of the original problem statement.

Runiowa is a fashion shoe company that tries to manufacture much more durable heels in 2020. The management team of Runiowa suggests two rubber materials A and B and the research team of Runiowa is asked to design an experiment to gauge whether the rubber A is more durable than the rubber B. 300 people in the US aged between 18 and 65 were randomly chosen. The rubber A is allocated at random to the right shoe or the left shoe of each individual. Then, the rubber B has been assigned to the other. For example, if Mr. Nathaniel is one of 300 people randomly chosen, then the right heel of Mr. Nathaniel is randomly assigned to be made with the rubber A and then his left heel is to be made with the rubber B. The research team measures the amounts of heel wear both the rubber A (wA) and the rubber B (wB) in each individual and records the difference wA − wB of 300 individuals. Even though the individuals are heterogeneous with different heights and weights, those individual heterogeneities will not obscure the comparison of treatment groups by focusing on the paired differences of each individual. Also as long as the heel materials are randomly assigned for each individual, there has been no restrictions on shoe styles. Note that the age of subjects is ranging from 18 to 65. In this way, researchers compare treatments within blocks controlling heterogeneity of individuals. The research team also repeats this experiment design with 300 people in the US aged between 18 and 65 chosen at random.

Question:

Is there a conjecture?

What is the response variable?

What is the explanatory variable?

What levels of the factor(s) were used in the expereiment?

What are the treatments for this experiment?

What are the experimental units?

What is the control?

Hoe much replication was used?

How was randomization used?

The data presented in Problem 7 are analyzed using multiple linear regression analysis and the models are shown here. In the models, the data are coded as 1 = new medication and 0 = standard medication, and age 65 and older is coded as 1 = yes and 0 = no. ŷ = 53.85 − 23.54 (Medication) ŷ = 45.31 − 19.88 (Medication) + 14.64 (Age 65 +) ŷ = 45.51 − 20.21 ( Medication ) + 14.29 ( Age 65 + ) + 0.75 ( Medication × Age 65 + ) Patients < 65 : ˆ y = 45.51 − 20.21 ( Medication ) Patients 65 + : ˆ y = 59.80 − 19.47 ( Medication ) Does it appear that there is effect modification by age? Justify your response using the preceding models.

Based on your answers to Problem 8 and Problem 9, how should the effect of the treatment be summarized? Should results be reported separately by age group or combined? Should the effect of treatment be adjusted for age? Justify your response using the models presented in Problem 9.

Problem 4

The following data exists for Lawrence Repair, a large equipment repair company. The behavior pattern of the maintenance overhead costs must be determined to prepare the annual profit plan for next year. The cost accountant has suggested using statistical analysis to derive an equation in the form of y=mx+b for maintenance overhead costs. Monthly data regarding past parts costs, repair hours and overhead costs are provided below.

Prepare a graphical representation of overhead cost estimation using Parts Cost as the independent variable. Using Repair Hours as the independent variable. For both scatterplots, use good formatting to include a Figure Title, Axis labels, trend line and remove blank area on the left half of the chart at a minimum.

Compute and report the simple regression results for each of the independent variables.

Compute and report a multiple regression analysis using both independent variables to explain the variation in costs. Provide a single cost equation using both independent variables.

Based on the single cost equation derived from the regression analysis, predict overhead costs for $3500 parts cost & 480 repair hours.

What is the percent of the total variance that can be explained by the regression equation?

13. A researcher assesses 7 students on test anxiety using blood pressure as a measure (the higher the blood pressure, the greater the anxiety); she then assesses the same subjects again after they view a 2-hour videotape on "relaxation techniques under stress". The results, average systolic blood pressure, were:

Subject Before After

1 120 110

2 160 110

3 124 100

4 135 99

5 170 115

6 143 106

7 188 89   

   1. State the independent and dependent variables.
   2. State the Null Hypothesis in words and symbols.
   3. Compute the appropriate statistic.
   4. What is the decision? reject
   5. State the full conclusion in words.

The Gallup Poll once asked a random sample of 1600 adults “Do you happen to do step aerobics?” Suppose that in fact 26% of all Americans do step aerobics.

a) What is the mean of the sampling distribution of proportions who do step aerobics?

b) What is the standard deviation the sampling distribution of proportions who do step aerobics?

c) Justify the distribution: HINT: Check that np and n(1-p) are greater than or equal to 10.

d) What is the probability that proportion of adults that do step aerobics is between 24% and 30%?

e) What is the probability of the proportion of adults that do step aerobics is more than 28%?

With individual lines at its various windows, a post office finds that the standard deviation for normally distributed waiting times for customers on Friday afternoon is 7.2 minutes. The post office experiments with a single, main waiting line and finds that for a random sample of 25 customers, the waiting times for customers have a standard deviation of 3.5 minutes.

With a significance level of 5 percent, test the claim that a single line causes lower variation among waiting times (shorter waiting times) for customers.

what is the p-value?

4S coronary mortality. The Scandinavian simvastatin survival study (4S) was a randomized clinical trial designed to evaluate the effects of the cholesterol-lowering agent simvastatin in patients with coronary heart disease. Over 5.4 years of follow-up, the treatment group consisting of 2221 individuals experienced 111 fatal heart attacks. The placebo group of 2223 individuals experienced 189 such events. Calculate the risks in the groups and test the difference for significance. In relative terms, how much did simvastatin lower heart attack mortality?