Hypothesis Test Steps: a) H_0 and H_1 and alpha b) Find the proper test statistic c) Find the critical region and critical value(s) d) Find the p-value e) State your decision based on b)-d) f) If you reject build the proper confidence interval Question 1: Individuals filing federal income tax returns prior to March 31 received an average refund of $105G. Consider the population of ?last-minute? filers who mail their tax return during the last five days of the income tax period. A sample of 400 ?last-minute? filers resulted in a sample mean refund of $910. Based on prior experience the IRS states the standard deviation is $1600. Is there evidence at a 5% level of significance that ?last-minute? filers on average received different refunds than do early filers? Question 2: Let us assume our null hypothesis is that the mechanic is honest and fixes the car?s issue. Also let us assume our alternative hypothesis is that the mechanic is not honest and does not fix the Car\'s issue but still charges us. a) What is the Type I error in this situation b) What is the Type II error in this situation Question 3: Annual per capita consumption of milk is 21.6 gallons in 2006. Being from the Midwest you would think the milk consumption would be different then the national mean. A sample of 35 individuals from the Midwest showed a sample mean annual consumption of 24.1 gallons with a standard deviation of 4.8 gallons. Is there evidence at a 4% level of significance that mean annual consumption in the Midwest is different from the national mean of 21.6 gallons? Question 4: The chamber of commerce of a Florida Gulf Coast community advertises that area residential property is available at a mean cost of $125,000 or less per lot. Suppose a sample of 32 properties provided a sample mean of $121,000 per lot and a sample standard deviation of $12,500. a) Is there evidence at a 5% level of significance to show the mean cost is less than $125,000? b) If you change to a 1% level of significance does this changes your result in part a) and explain your reasoning.
Question 1)
Mean =1056
SD = 1600
X-bar = 910
n =400
alpha =0.05
z = (X-bar - Mean)/(SD/sqrt(n))
= (910 - 1056)/(1600/sqrt(400))
= -1.83
P-value = 0.0336 Answer
Since ,
P < 0.05
Reject null hypothesis.
Question 2)
a) Type I error : The mechanic is honest and fixes the car but infact he is not honest.
b) Type II error : The mechanic is honest but not fixes the car.
Question3)
Mean =21.6
SD = 4.8
X-bar = 24.1
n =35
alpha =0.04
z = (X-bar - Mean)/(SD/sqrt(n))
= (24.1 - 21.6)/(4.8/sqrt(35))
= 3.08
P-value = 0.9990 Answer
Since ,
P > 0.04
Failed to reject null hypothesis , there is not sufficient evidence .
Question 4)
Mean = 125000
n=32
X-bar = 121000
SD = 12500
z = (X-bar - Mean)/(SD/sqrt(n))
= (121000 - 125000)/(12500/sqrt(32))
= -1.81
P-value = 0.0351
a) P < 0.05. Hence reject null hypothesis.
b) Yes , P > 0.01 . Hence failed to reject null hypothesis , there is not sufficient evidence .
Homework Sourse
