The proportion of adults living in a small town who are college graduates is estimated to be p=0.3. To test this hypothesis, a random sample of 200 adults is selected. If the number of college graduates in the sample is anywhere in the fail-to-reject region defined to be 52 sxs 68, where x is the number of college graduates in our sample, we shall not reject the null hypothesis that p = 0.3; otherwise, we shall conclude that p #0.3. Complete parts (a) through (c) below. Use the normal approximation. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) Evaluate a assuming that p = 0.3. a=0.1896 (Round to four decimal places as needed.) (b) Evaluate ẞ for the alternatives p=0.2 and p = 0.4. For the alternative p=0.2, p = 0.0210 (Round to four decimal places as needed.) For the alternative p = 0.4, ẞ= 0.0484 (Round to four decimal places as needed.) (c) Is this a good test procedure? Consider a value of a to be relatively small if it is less than 0.1000 and relatively large if it is greater than 0.1000. This a good test procedure, because while a is relatively small, at least one ẞ is relatively large. while both values of ẞ are relatively small, a is relatively large. all values of a and ẞ are relatively large. all values of a and ẞ are relatively small.
The proportion of adults living in a small town who are college graduates is estimated to be p=0.3. To test this hypothesis, a random sample of 200 adults is selected. If the number of college graduates in the sample is anywhere in the fail-to-reject region defined to be 52 sxs 68, where x is the number of college graduates in our sample, we shall not reject the null hypothesis that p = 0.3; otherwise, we shall conclude that p #0.3. Complete parts (a) through (c) below. Use the normal approximation. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) Evaluate a assuming that p = 0.3. a=0.1896 (Round to four decimal places as needed.) (b) Evaluate ẞ for the alternatives p=0.2 and p = 0.4. For the alternative p=0.2, p = 0.0210 (Round to four decimal places as needed.) For the alternative p = 0.4, ẞ= 0.0484 (Round to four decimal places as needed.) (c) Is this a good test procedure? Consider a value of a to be relatively small if it is less than 0.1000 and relatively large if it is greater than 0.1000. This a good test procedure, because while a is relatively small, at least one ẞ is relatively large. while both values of ẞ are relatively small, a is relatively large. all values of a and ẞ are relatively large. all values of a and ẞ are relatively small.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 31PPS
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