Question

N-200 x = 30 12=0.01 Example # 6 Nationwide 13.7% of employed wage and salary workers are union members. At random sample of 200 local wage and salary workers showed that 30 belonged to a union. At 0.01 level of significance, is there sufficient evidence to conclude that the proportion of union members differs from 13.7%? Step 1: Write the null hypothesis and the alternative hypothesis and identify the claim. Hoop = 13.78 claim) AND HEP# 13.790 Step 2: Find the critical value(s): C.v. + 1.96 Step 3: Find the test value: 30 = 0.15 P=13.7 951-p=1-13.75 -12.7 = z - Pop JPq/N 0.15-13.7 11,3,7) (12.7/200 Step 4: Make the decision. Step 5: Summarize the result 11 iki

Answer 1

wees. hypothes. Ho alternatives of union members in population is 13.7% het po be propantion of employed wage wouters melha are union members In the popullation het p he puespoution of name in the sample Then accouding to question, Null Ho: Por 13 7 ie the proportion : H: Po 13-7/100 ull the peopsution. hypothes of union members is not 13.7 % NOVO, 200 sample size). saneple, peoportion Qo = I-Po I-los ) - 0.137 0.863 Text datutic (for clitical values 2- y since N NOU cundarge} m 30 200 undur Ho b - P. Podo/n = 0.15 -0.137 0.137 X0-863 200 1) ☺ .013 0.013 0.00059 0.0243 Conduion = 0.5349 duel of = 0 - 0 1 Letab = 2.58 Pfuomo andable jou Ical = 0.5349 Thus, 17 cal) < 1 tabl. Ho may not be Mientiel 2 dailed tut?

0.99 2=0.005 190.005 -Zrab zal 4258 90.53 Result: At x=0.01 be the null 2 wypothesis may not ewidence anglainst null boy gothers. Thus, there pested die there is proper I sufficient evidence to conclude that proportion of differs from is no Tunion Members 13.7%

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