Section 7.3: Hypothesis Testing for Mean (SmallSamples) 1. A local tire store su
ID: 2955402 • Letter: S
Question
Section 7.3: Hypothesis Testing for Mean (SmallSamples)
1. A local tire store suspects that themean life of a new discount tire is less that 39,000 miles. Tocheck the claim, the store selects randomly 18 of these newdiscount tires. When they are tested, it is found that the meanlife is 38,250 miles with a sample standard deviation s = 1200miles. Assume the distribution is normally distributed.
a. Use the critical value t0 method from the normaldistribution to test for the population mean m. Test thecompany’s claim at the level of significance a = 0.05.
1. H0:
Ha :
2. a=
3. Teststatistics:
4. P-value orcritical z0 or t0.
5. RejectionRegion:
6. Decision:
7. Interpretation:
b. Use the critical value t0 method from the normaldistribution to test for the population mean m. Test thecompany’s claim at the level of significance a = 0.01
1. H0:
Ha :
2. a=
3. Teststatistics:
4. P-value orcritical z0 or t0.
5. RejectionRegion:
6. Decision:
Explanation / Answer
1. H0: >=39,000
Ha : <39,000
2. a =0.05
3. Teststatistics:
t=(xbar-)/(s/n)
=(38250-39000)/(1200/sqrt(18))
= -2.65
4. P-value orcritical z0 or t0.
t(=0.05,df=n-1=17)=-1.7396 (check student ttable)
The criticalvalue t=-1.7396
5. RejectionRegion:
t<-1.7396
6. Decision:
Sincet=-2.65<-1.7396, we rejectHo.
7. Interpretation: