Answers to Practice Questions 7.4, 7.10, 7.16 (8.4, 8.10, 8.16) Use the decision tree to help decide which test to use!

Healey #7.4/8.4 Problem information: Use the 5-step method….  = 453 = 502 σ = 95 (note: question gives pop’n value) n = 152 Use the 5-step method…. Steps 1 - 3 1 random sample, Interval-ratio Sample is large n ≥ 100, normal z-test Question asks “Is there a significant difference?” 2-tailed test, α=.05, z=±1.96 Ho: H1:

#7.4/8.4 cont. Step 4: Step 5: Zobtained>Zcritical therefore reject Ho The difference is significant and not random chance The first year students’ score is significantly different from the national population (Zobt=6.36, α=.05)

Healey #7.10/8.10 Problem information: Use the 5-step method….  = $130 = $98 s = $5 (question gives sample value) n = 36 Use the 5-step method…. Steps 1 - 3 1 random sample, Interval-ratio Sample is small, n < 100, t-distribution t-test Question asks “Is the a difference significant?” 2-tailed test, df=n-1=35, α=.05, t=±2.042 (more conservative) Ho: H1:

Healey #7.10/8.10 cont. Step 4: Step 5: tobtained>tcritical therefore reject Ho The difference is significant and not random chance Property tax for the sample is significantly different from the national population (tobt=-37.86, df=35, α=.05)

Healey 7.16/8.16 Problem information: Use the 5-step method…. Pu = .18 (18%) Ps = .217 (21.7%) N = 323 Use the 5-step method…. Steps 1 - 3: 1 random sample, Nominal Sample is large n ≥ 100, normal z-distribution (z-test) Question asks “is the difference significant?” 2-tailed test, α=.05, z=±1.96 Ho: Ps=Pu H1:Ps≠Pu

#7.16/8.16 cont. Step 4: Step 5: Zobtained<Zcritical therefore fail to reject Ho The difference is not significant and is random chance There is no significant difference in unemployment rates. note that if a one-tailed test had been used instead (i.e. to test if the sample unemployment rate is higher) then Zcritical=+1.65, and Ho would be rejected!