Name__________________



Name__________________ MIS 214 Statistics II

2013/2014 Spring Final

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No calculator exchanges are allowed.

1 (20 pt) Independent random samples of BS (batchelor of science) and MA (master of arts) degree holding MIS graduates are questioned about the duration of their first jobs. For a sample of 44 BS degree holders mean duration of their first job is 35.02 months and the sample standard deviation was 18.2. For a sample of 68 MA degree holders mean duration of their first job is 36.34 months and the sample standard deviation was 18.3. Test at a 10% significant level against a two sided alternative, the null hyphotheisis that the population means of the duration of the first jobs are the same for the two groups of MIS graduates.(assume that population variance’s are equal)

2. (15 pt) X and Y are two continuous variables for which n observations are available. Let b1 be the slope of the least square regression of Y on X (dependent variable Y, explenatory variable X ), b*1 be the slope of the least square regression of X on Y(dependent variable X, explenatory variable Y ), r be the sample correlation betwen X and Y.

a) Write the population and sample regression models for the two cases

b) Show that b1.b*1= r2

3. (15 pt) The following regression is estimated to predict households milk consumption

Y = -0.025 + 0.052X1 + 1.14X2

Y: milk consumption

X1:weekly income

X2: familiy size

SST and SSR are as follows SST = 162.1, SSR = 88.2

A third independent variable; X3 : number of preschool childeren in the family, was added to the regression model and when estimated SSE (sum of square error) of the new regression was found to be 83.7. Test the null hypothesis that, all other things being equal, number of preschool childeren in the family does not affect milk consumption.

4. (15 pt) A random sample of 150 residents was asked to indicate their first preference for one of three television satations (shown bellow). Test the null hypothesis that for the population the first preferences are evenly distributed among the three satations.

Station A B C

# first preference 47 42 61

5. (15 pt) Consider the one-way analysis of variance set up

a) Show that the within-group sum of squares can be wtritten as follows: K

SSW = ( Ki=1( nij=1x2ij - n(Ki=1 x2i

b) Show that the between-group sum of squares can be wtritten as follows: K

SSG = ( Ki=1 nix2i - nx2

c) Show that the total sum of squares can be wtritten as follows: K

SST = ( Ki=1( nij=1x2ij - nx2

6. (20 pt) An instructor in an economics class is considering three different texts. He is also considering three types of examinations – multiple choice, essay, and a mix of multiple choice and essay questions. He teachs nine sections and randomly assigns a text – examination type combination of each section. He obtained students’ evaluations for each section as shown below

Text

Examination A B C

Mulitrjple choice 4.8 5.3 4.9

Essays 4.6 5.0 4.3

Mix 4.6 5.1 4.8

a) Write the population model and estimate the values of ( , Bis and Gis for i=1,2,3

b) Prepare the two-way analysis of variance table

c) Test the null hypothesis of equality of population mean ratings for the three texts

d) Test the null hypothesis of equality of population mean ratings for the three examination types

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