Question

The Arizona Department of Transportation (ADOT) is considering changing statewide speed limits from 65 mph to 75 mph. They wish to perform analysis on p, the proportion of Arizona residents that favor this change. In order to prove that a majority of residents favor the change, ADOT wishes to test the following hypotheses using a level of significance of 0.05. Ho:p = 0.5 H:p > 0.5 ADOT wishes to design the test to have a power of 90% if the true population proportion is equal to 0.55. Part a (5 points): How many residents should be surveyed? You may use this sample size for the remainder of this problem. (Note: You should get a value between 800 and 900 on this part. If you did not, then choose a value between 800 and 900 and use it to work the remainder of the problem.)

Answer 1

The sample size is calculated using the formula mentioned. The critical values are obtained from STATKEY (image attached for reference).

This is a Ore sided test. 2 Sample size (n) = Z 1-2 + Z 21-ß ES Where ES (Effect size) pi-po ſpoli-po) In the given question, d= 0.05 1-0 = 0.95 1.645 source of critical 21-2= 20.95 = 1-ß (power) 21-6 = 20.90 0.90 Value': T1-83 Calculatoa 1.282 po= 0.5g P = 0.55 Sog Es= 0.55 - 0.5 0.1 0.5 x 0.5 2 .. ma sample size) = (1.645 + 1-282) (1.45 = 856.7 0.1 (w8 857 Hence, 857 residents must be surveyed.