Question

SHOW WORK, FOR PRACTICE.

1B)

EWEX has been working with utility companies to set up expensive power generating windmills. In order for a site to be effective, the average wind speed must be more than 20 mph. At a specific site, EWEX took a sample of forty-five wind speed readings. The sample average wind speed is 21.7 mph with a standard deviation of 4.2 mph. EWEX will only build the windmill if they are sure that the true average wind speed is greater than 20 mph. Should they build the windmill? Justify by conducting a hypothesis test at α = 0.05.

1C).

For problem 1B, Describe in the words of the problem what making a Type I error would be and its likely consequences. For problem 1B, Describe in the words of the problem what making a Type II error would be and its likely consequences.

6A)

MPP Batteries are supposed to last at least 3 years. A consumer advocate collects a random sample of 200 of these batteries and finds that 186 last at least 3 years. Does this provide evidence at the 5% significance level to support the claim that less than 95% of all Interstate batteries last at least 3 years? Justify by running a hypothesis test.

Answer 1

Answer 1 (0 : Given n 45 here is wird speees, i.e. n is the wind The variable n = 21.7 mph S=4.2 mph we 4 = 20 mph have to test Hou l = 4 vs M : ñ > 4 The to test the above hypothesis is test statistic t-test. one-sample. M to n- s with no 1 d. f. t 21.7-20 = 4.21 kus t = 1.7xrus 4.2 It = 2.72 with undf. The p-value for above test is 0.0047. The obtained p-value is oos which suggests that we have strong evidence against to to reject it and we can conclude that sample average wind speed is more than 20 mph and also We can consult that they should built the it windmill

Answer - 6(A) & here the random vanase we are interested in lest at least 3 years. is age of a number of batteries which 2 Cinen n= 200 x = 186 P=0.95 l population proportion) &= 0.05 The sample proportion is p. = 16 140=0.93] We have to test Mor p =P ve Haste p <P the test statistic to test the above hypothesis is a below test as php z = 0,93- 0.gs Za 0.9311-0.93) 200 2 0.02x 200 $0.9370.07 Z= 1.10855 The p-value for above test is 0.1338 which sugust that we do not enough evidence against to to reject it and we can conclude that there is no evidence to claim that less than gst. att interstate batteries Tast at least 3 years