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STA 100 Take Home Part of Final Due at final exam Prof. Thistleton
Solve each of the following two problems by hand, and then use SPSS to support your answers. Hand in your SPSS printout and indicate the relevant results on the printout by circling or highlighting and labeling these results.
- The following data were obtained in an experiment designed to check whether there is a systematic difference in the weights (in grams) obtained with two different scales. Several specimens were weighed with the first scale and then again with the second scale. Test at the α = 0.01 level of significance whether there is a significant difference between the average weights obtained with the two scales.
Rock Specimen scale 1 scale 2 di d^2 i 1 9.5 10. 2 8.3 11. 3 10.1 10. 4 10.2 13. 5 8.8 10.
- A sample of n = 5 men was formed and the following data (rounded for convenience) concerning pinkie length and index finger length were obtained.
Index, x Pinkie, y x^2 xy y^2 2.9 2. 2.8 2. 3.2 2. 3.0 2. 3.3 2.
Calculate the estimated slope, b, the estimated intercept, a, and the estimated correlation coefficient, r. What does your model predict for the pinkie length of an individual with an index finger length of 3 inches?
STA100 Final Exam December 13, 2006 Prof. Thistleton
- You have collected the following summary data: x = 24, n = 25, and s = 3.
(a) Test the null hypothesis H 0 : μ = 25 against the alternative H 1 : μ < 25 at the α = 0.01 level of significance. Report a p-value for this test.
(b) Construct a 99% confidence interval for population mean for the data given above.
(c) Suppose you have a population with standard deviation σ = 3. How large a sample size should you take to estimate the true population mean μ if you need your maximal margin of error to be E = 1.5 and you would like to be 95% confident of your result?
- The following SAT scores were obtained from a sample of freshmen entering a college:
xi x^2 i 457 333 513 529 385
(a) Calculate the mean x and the standard deviation, s for this sample.
(b) Test at the α = 0.05 level of significance whether the population mean is μ = 500 against the alternative μ 6 = 500. Approximate a p-value.
(c) Calculate a 90% confidence interval for the population mean μ.
- There are two patient populations in your clinical practice. You wish to test to see whether these two populations have the same mean score on the Life Orientation Test. You administer the test to 23 patients from the first population and obtain a mean score of 19.5 and a standard deviation of
- The sample from the second population is of size 28 and has a mean score of 22 with a standard deviation of 4. Test at the α = 0.05 level of significance whether the two populations have the same mean.
- Suppose that you believe that a person’s level of optimism influences their susceptibility to disease and that you have a way to distinguish optimists and pessimists. You infect 100 optimists and 100 pessimists with a cold virus and obtain the following data.
Personality Became Sick Optimist Pessimist Yes 38 52 No 62 48
Personality Became Sick Optimist Pessimist Yes No
Test at the α = 0. 01 los whether or not you believe that optimists and pessimists become ill at the same rate using the RxC/Contingency Table method. Approximate a p-value.
