Self-Employment According to the Bureau of Labor Statistics, 10.1 % of Americans are self-employed. A researcher wants to determine if the self-employment rate in a certain area is different. She takes a random sample of 500 working residents from the area and finds that 62 are self-employed. a. Test the hypothesis that the proportion of self-employed workers in this area is different from 10.1 % . Use a 0.05 significance level. b. After conducting the hypothesis test, a further question one might ask, “What proportion of workers in this area are self-employed?” Use the sample data to find a 95 % confidence interval for the proportion of workers who are self-employed in the area from which the sample was drawn. How does this confidence interval support the hypothesis test conclusion?
Self-Employment According to the Bureau of Labor Statistics, 10.1 % of Americans are self-employed. A researcher wants to determine if the self-employment rate in a certain area is different. She takes a random sample of 500 working residents from the area and finds that 62 are self-employed. a. Test the hypothesis that the proportion of self-employed workers in this area is different from 10.1 % . Use a 0.05 significance level. b. After conducting the hypothesis test, a further question one might ask, “What proportion of workers in this area are self-employed?” Use the sample data to find a 95 % confidence interval for the proportion of workers who are self-employed in the area from which the sample was drawn. How does this confidence interval support the hypothesis test conclusion?
Solution Summary: The author explains how to perform a z-test to determine whether the population proportion is different from 10.1 or not.
Self-Employment According to the Bureau of Labor Statistics,
10.1
%
of Americans are self-employed. A researcher wants to determine if the self-employment rate in a certain area is different. She takes a random sample of 500 working residents from the area and finds that 62 are self-employed.
a. Test the hypothesis that the proportion of self-employed workers in this area is different from
10.1
%
.
Use a
0.05
significance level.
b. After conducting the hypothesis test, a further question one might ask, “What proportion of workers in this area are self-employed?” Use the sample data to find a
95
%
confidence interval for the proportion of workers who are self-employed in the area from which the sample was drawn. How does this confidence interval support the hypothesis test conclusion?
1.2.17. (!) Let G,, be the graph whose vertices are the permutations of (1,..., n}, with
two permutations a₁, ..., a,, and b₁, ..., b, adjacent if they differ by interchanging a pair
of adjacent entries (G3 shown below). Prove that G,, is connected.
132
123
213
312
321
231
You are planning an experiment to determine the effect of the brand of gasoline and the weight of a car on gas mileage measured in miles per gallon. You will use a single test car, adding weights so that its total weight is 3000, 3500, or 4000 pounds. The car will drive on a test track at each weight using each of Amoco, Marathon, and Speedway gasoline. Which is the best way to organize the study?
Start with 3000 pounds and Amoco and run the car on the test track. Then do 3500 and 4000 pounds. Change to Marathon and go through the three weights in order. Then change to Speedway and do the three weights in order once more.
Start with 3000 pounds and Amoco and run the car on the test track. Then change to Marathon and then to Speedway without changing the weight. Then add weights to get 3500 pounds and go through the three gasolines in the same order.Then change to 4000 pounds and do the three gasolines in order again.
Choose a gasoline at random, and run the car with this gasoline at…
AP1.2 A child is 40 inches tall, which places her at the 90th percentile of all children of similar age. The heights for children of this age form an approximately Normal distribution with a mean of 38 inches. Based on this information, what is the standard deviation of the heights of all children of this age?
0.20 inches (c) 0.65 inches (e) 1.56 inches
0.31 inches (d) 1.21 inches
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