Question

5. Suppose researchers have reported that the population mean for the annual salary of certified welders was $40,000, and the population standard deviation was $5200. A new survey of 200 welders was taken, and the mean annual salary of this sample was $39,000. At the 0.05 significance level, can we conclude that the mean annual salary of certified welders is less than $40,000? Complete steps 1 through 6 below. STEP 1. State the null hypothesis and the alternate hypothesis. (worth 4 points) STEP 2. State the level of significance. (worth 2 points) STEP 3. State the test statistic. (worth 2 points) STEP 4. Formulate the decision rule. (worth 4 points) STEP 5. Make a Decision. Please show your work. (worth 6 points) STEP 6. Determine the p-value (please show your work); interpret the result of the hypothesis test. (worth 4 points)

Answer 1

page-I X: Annual salary of certified Welders population mom = = $40,000 population standard deviation=0 = $5200 A new survey of 200 welders taken 1.e. n = 200 Sample Mean = * = $ 39,000 220.06 We want to test that the mean annual salary of cortified welders is less than $40,000 lie. ea $40,000 stept! Ney & Alternative hypothesi's Ho: U= 40,000 ( there is no enough evidence to conclude that annual salary of Certified weldee is less than $ 40000 He: 4 <40,000 ( there is significant evidence to conclude that annutal callary of cortified welder is less than $40,000) step2: level of significance Exe = 0.05 steps: Here population standard deviation is given so go with ex- test. .: Test statistic (2)= Hello 6) in 39,000 - 40,000 - .:under Ho 5200/v2oo 12=40000} - 1000 367.6955 -2.7196

page-II Test statistics () = -2.7196 .: step 4: Decision Rule: If - Lal > - Ktab then we reject null hypothesis (Ho) Totab = 20.05 = 1:645 9.XUN 0,1)} Here -(-2.7196) > - 4.645 lie. 2.7196 > -1.645 80 Here hele i el grejeet the nw hypothesis (HO) step 5. != kle goject the hell hypothesis (HO) step 6 - p-value p-value = P(X<-/Kcall) = P(Z < -1 -2.4961) - P(X5-254196) = 0.008268 $ .! KUNCOI)} Here p-value a x then we reject Ho 80 p-value = 0.008268 <d=0:05 so We reject Ho Interpretation - There is a enough ovidence to conclude that annual sallay of certified Welder is less than $ 40,000