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# Statistics Module 3: Understanding Inference Problems and Solutions

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• Statistics Module 3: Understanding Inference Problems and Solutions

Refer to the tutorial on Inference before attempting the questions.

Statistics Module 3: Understanding Inference

Q1.

For a population with a known variance of 185, a sample of 64 individuals leads to 217 as an estimate of the mean. (Levin & Rubin)

1. Find the standard error of the mean
2. Establish an interval estimate that should include the population mean 68.3 percent of the time.

Q2.

Consider the data of VIX index population sample sheet. The standard deviation of the population is 9.24. Take two samples of 200 and 300 from the VIX population sample. Attached sheet here. Stats 3 Practice and Solution Sheet

1. Calculate the standard error of the mean for both these samples for the VIX close price
2. Establish a 90 % C.I. for their respective VIX close price means (refer to the attached data sheet for sample)

Q3.

Calculate the running mean for VIX closing price for both the sample sheets. Compare the running mean as the sample size increases and compare the change in the closing price with the mean of the closing price of the population sample (18.72).

Q4.

The school board of Foresight county considers its most important task to be keeping the average class size in Foresight country schools less than the average class size in neighboring Hindsight County. Miss Dee Marks, the school superintendent for Foresight County, has just received reliable information indicating the average class size in Hindsight County this year is 30.3 students. She does not have figures for all 621 classes in her school system, so she is forced to reply upon the data from 76 classes that have reported class sizes, yielding an average class size of 29.8 students. Dee knows that the class size of Foresight County classes has a distribution with an unknown mean and standard deviation equal to 8.3 students. Assuming the sample size of 76 that Miss Marks possesses is randomly closes from the population of all Foresight County class sizes: (Levin & Rubin)

a. Find an interval that Dee can be 95.5 percent certain will contain the true mean.

b. Do you think Dee has met her goal?

Q5.

For VIX sheet calculate population mean and standard deviation for VIX low values. Repeat Q2 for VIX low values.

Q1.

σ   = 13.60, n = 64

a. Standard error of the mean = 1.70            b. (215.3, 218.7)

Q2.

1. Standard error of the mean (0.65, 0.53)
2. (11.45, 13.59) and (12.06 and 13.80) Use Norm.inv (0.05,0,1) for C.I. 90% | Refer the excel attachment

Q3.

Refer to the sheet.

Q4.

Confidence Interval (27.90, 31.70)  Refer to the excel attachment for solution

Standard error of the mean= 0.95

Its not clear from the C.I whether Dee has met her goal since the true mean could be more than 30.3 which is the mean of Hindsight County for class size.