MATH227 Fall 2009 HWK#08
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1- The following data is sampled from a normal population.
Male / FemaleA- To test the average age of males and females are significantly different (use 0.03 level of significant).
B- Also construct the 97% confidence interval for the difference of the means of the populations.
2- The following data is sampled from a normal population. Assume.
Male / FemaleA- To test the average age of males and females are significantly different (use 0.02 level of significant).
B- Also construct the 98% confidence interval for the difference of the means of the populations.
3- The following data is sampled from a normal population. Assume.
Male / FemaleA- To test the average age of males and females are significantly different (use 0.02 level of significant).
B- Also construct the 98% confidence interval for the difference of the means of the populations.
4- A Secchi disk is an eight-inch diameter weighted disk that is painted black and white and attached to a rope. The disk is lowered into water and the depth (in inches) at which it is no longer visible is recorded. The measurement is an indication of water clarity. A environmental biologist is interested in determining whether the water clarity of the lake at Joliet Junior College is improving. She takes measurements at the same location on the same dates during the course of a year and repeats the measurements on the same dates five years later. She obtains the following results:
Observation / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8Initial Depth / 45 / 55 / 60 / 70 / 50 / 40 / 60 / 55
Depth 5 Years Later / 50 / 65 / 65 / 68 / 45 / 44 / 62 / 55
A- Test the claim that the clarity of the lake is improving at the α = 0.05 level of significance.
B- Construct a 90% confidence interval about the population mean difference. Interpret your results.
5- Blood clotting occurs due to a sequence of chemical reactions. The protein thrombin initiates blood clotting by working with another protein, prothrombin. It is common to measure an individual’s blood clotting time through prothrombin time-the time between the start of the thrombin-prothrombin reaction and the formation of the clot. Researchers wanted to study the effect of aspirin on prothrombin time. They randomly selected 10 subjects and measured the prothrombin time (in seconds), first without taking aspirin and again three hours after taking two aspirin tablets. They obtained the following data:
Subject / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10With Aspirin / 12.5 / 12.1 / 12.2 / 12.8 / 12.2 / 12.6 / 10.8 / 11.5 / 12.1 / 11.2
Without Aspirin / 12.2 / 12.4 / 12.7 / 12.9 / 12.2 / 12.2 / 11.3 / 10.9 / 12.1 / 11.8
A- Test the claim that aspirin affects the time it takes for a clot to form at the α = 0.05 level of significance. Note: A normal probability plot and box-plot of the data indicate that the differences are approximately normally distributed with no outliers.
B- Construct a 95% confidence interval about the population mean difference. Interpret your results.
6- An engineer wanted to know whether the strength of two different concrete mix designs differed significantly. He randomly selected 9 type A and 12 type B. The results are as follows:
Type A / Type B3990 / 4080 / 3800 / 4070 / 4890 / 5020 / 4330
3870 / 3200 / 3780 / 4640 / 5220 / 4190 / 3730
4080 / 4040 / 2940 / 4120 / 4620 / 4600 / 4500
A- Test the claim that mixture type A is different than mixture Type B at α = 0.02 level of significance.
B- Construct a 98% confidence interval about μ1 – μ2 and interpret the results.
7- A nutritionist claims that the proportion of females who consume too much saturated fat is lower than the proportion of males who consume too much saturated fat. In interviews with 600 randomly selected females, she determines that 300 consume too much saturated fat. In interviews with 700 randomly selected males, she determines that 400 consume too much saturated fat, based upon data obtained from the USDA’s 1994-1996 Diet and Health Knowledge Survey.
A- Test the claim that a lower proportion of females than males consume too much saturated fat at the α = 0.05 level of significance, using both the classical approach and P-value approach.
B- Construct a 90% confidence interval for the difference between the two population proportions.
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