3) The expenditures (in dollars) per pupil for states in three sections of the c

Question

3) The expenditures (in dollars) per pupil for states in three sections of the country are listed. Using a 0.04 significance level, can we conclude that there is a significant difference between regions? Assume normally distributed variables with equal variances Eastern third 4946 5953 6202 7243 6113 Middle third 6149 7451 6000 6479 Western third 5282 8605 6528 6911 4) In a sample of 100 store customers, 43 used a MasterCard. In another sample of 120 customers. 59 used a Visa card. Find the 95% confidence interval for the difference in proportions of customers who use either card. 5) A sample of 15 students are tracked for the first two years of college, with each student's financial aid award for both years shown below: Fr $25K 31 22 15 17 23 20 18 26 33 27 28 30 26 26 So $27K 33 21 14 12 20 22 17 25 22 34 17 33 26 20 Find a 95% confidence interval for the true mean difference in years. Assume that both years' financial aid awards are approximately normally distributed. Two groups are given a problem-solving test, and the results are compared. Find a 98% confidence interval for the true mean difference in scores. 6) Math Majors Sample mean-89.3 Sample standard deviation=5.1 Computer Science Majors Sample mean-81.1 Sample standard deviation-4.2 Sample size-60 | Sample size=51

Explanation / Answer

3:

Here we need to compare more than two populaitons means so one way ANOVA will be used.

Hypotheses are:

H0: The populaitons mean expenditure is same for all three regions.

Ha: At least one populaitons mean expenditure differ.

Following is the output of one way ANOVA:

The p-value is:

p-value = 0.5433

Since p-value is greater than 0.04 so we reject the null hypothesis.

That is we cannot conclude that there is signifcant difference between regions.

Anova: Single Factor SUMMARY Groups Count Sum Average Variance Eastern third 5 30457 6091.4 667494.3 Middle third 4 26079 6519.75 425494.25 Western third 4 27326 6831.5 1881561.667 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 1244587.973 2 622293.9865 0.648821376 0.543326405 4.102821 Within Groups 9591144.95 10 959114.495 Total 10835732.92 12

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