STAT 112 FINAL EXAMINATION
2011-2012
Duration is 100 minutes. You may use a calculator but you cannot share it.
1.
(10 points)Express the following claims in symbols.
a. Alcohol concentration of wine is greater than beer.
𝜇𝑤𝑖𝑛𝑒 > 𝜇𝑏𝑒𝑒𝑟
𝑜𝑟
𝐻0 : 𝜇𝑊 − 𝜇𝐵 = 0
𝐻1 : 𝜇𝑊 − 𝜇𝐵 < 0
2.
b.
The proportion of people that prefer drinking beer is more than those that prefer wine.
c.
𝑝𝑏𝑒𝑒𝑟 > 𝑝𝑤𝑖𝑛𝑒
Men are more likely than women to have lung cancer.
d.
𝐻0 : 𝑝𝑀 − 𝑝𝑊 = 0
𝐻1 : 𝑝𝑀 − 𝑝𝑊 < 0
Vitamin content of bread is same immediately after baking and 3 days after baking.
𝜇𝑑 = 0
(20 points)You’re an economist for the Department of Labor. You’re studying unemployment rates. In Istanbul,
184 of 1500 people surveyed were unemployed. In Izmir, 129 of 1500 were unemployed. At the 0.05 level of
significance, can we say that Istanbul and Izmir have same unemployment rates? (ZERO points if hypotheses are
not stated in symbolic form!!!) (Hint: z values are at the bottom of the t-table)
𝐻0 : 𝑝𝑖𝑠𝑡 − 𝑝𝑖𝑧 = 0
𝐻1 : 𝑝𝑖𝑠𝑡 − 𝑝𝑖𝑧 ≠ 0
184
𝑝̂𝑖𝑠𝑡 =
= 0.1226
1500
129
𝑝̂𝑖𝑧 =
= 0.086
1500
𝑛𝑖𝑠𝑡 𝑝𝑖𝑠𝑡 , 𝑛𝑖𝑠𝑡(1−𝑝𝑖𝑠𝑡) , 𝑛𝑖𝑧 𝑝𝑖𝑧 , 𝑛𝑖𝑧 (1 − 𝑝𝑖𝑧 ) > 5
(𝑝̂𝑖𝑠𝑡 − 𝑝̂𝑖𝑧 ) − 0
𝑧=
= 3.290787
𝑝̂𝑖𝑠𝑡 (1 − 𝑝̂𝑖𝑠𝑡 ) 𝑝̂𝑖𝑧 (1 − 𝑝̂𝑖𝑧 )
√
+
𝑛𝑖𝑠𝑡
𝑛𝑖𝑧
𝑧𝑐𝑟𝑖𝑡 = ±1.96
REJECT NULL HYPOTHESIS
3.
(40 points)You work in Human Resources. You want to see if there is a difference in test scores after a training
program. You collect the following test score data:
At the 0.01 level of significance, was the training effective? (ZERO points if hypotheses are not stated in symbolic
form!!!)
𝐻0 : 𝜇𝑑 = 0
𝐻0 : 𝜇𝑑 ≠ 0
μd = 1 𝜎𝑑 = 6.53
1−0
𝑡=
= 0.31
6.53
2
Do Not Reject NULL HYPOTHESIS
4.
(20 points) A cellular phone company representative argues by observing daily traffic data in the server in Yasar
Üniversitesi that daily number of text messages send by students is more than 15. Test his claim with 90%
confidence. Data is collected from 64 students. Sample average is 11 and sample standard deviation is 3. All steps of
hypothesis testing must be shown properly. Write H0 and H1. Calculate test statistic. Write the conclusion. (Hint: z
values are at the bottom of the t-table)
𝐻0 : 𝜇 = 15
𝐻1 : 𝜇 < 15
𝑥̅ = 11, 𝑠 = 3, 𝑛 = 64
11 − 15
𝑧=
= −10.67
3
8
𝑧𝑐 = −1.282
REJECT NULL HYPOTHESIS
5.
(30 points)You work as a researcher in Department of Education. You want to find out if there is a difference in
spending per pupil between urban and rural high schools. Data is as follows:
Urban
Rural
15
15
Number
6012
5832
Mean
602
497
St Dev
Is there a difference in population means (𝛼 = 10%)
6.
(20 points) Does an average box of cereal contain 368 grams of cereal? A random sample of 25 boxes showed 𝑥̅ =
372.5. The company specified 𝑠 2 = 25 grams. Test at the 0.05 level of significance.
7.
(20 points) Write the working principle of a smoke detector in hypothesis testing formulation. What are Type I and
Type II errors?
𝐻0 : 𝑇ℎ𝑒𝑟𝑒 𝑖𝑠 𝑛𝑜 𝑓𝑖𝑟𝑒(𝑠𝑚𝑜𝑘𝑒)
𝐻1 : 𝑇ℎ𝑒𝑟𝑒 𝑖𝑠 𝑓𝑖𝑟𝑒 (𝑠𝑚𝑜𝑘𝑒)
Type 1 Error: Trigger alarm although there is no fire (smoke)
Type 2 Error: Not trigger alarm although there is fire (smoke)