(a) A trucking firm suspects the claim that the average lifetime of check the cl
ID: 3294076 • Letter: #
Question
(a) A trucking firm suspects the claim that the average lifetime of check the claim, the firm puts 20 of these tires on its trucks and gets a mean lifetime of 27, 463 miles with a standard deviation of 1, 348 miles. What can it conclude if the probability of a type-1 error(alpha) is to be most 0.01? (b) A random sample of 45 bottles of Sprites filled, on average 5.35 ounces with a standard deviation of 0.48 ounce. Test the hypothesis that mu = 5.5 ounces against alternative hypothesis mu notequalto 5.5 at a significance level (alpha) of 0.011. Also, calculate p-value for this case.Explanation / Answer
a)
Hypothesis:
H0 : mu <= 28000
Ha : mu > 28000
Test statistic:
x = 27463 , s = 1348 , n = 20
t = ( x - mean) / ( s/sqrt(n))
= (28000 - 27463)/(1348/ sqrt(20))
= 1.7816
P value is calculated using t = 1.7816 , df = 19
p value = 0.0454
As p-value is greater than the significance level of 0.01, we fail to reject the null hypothesis.
This means there is not sufficient evidence to conclude that the average livetime of tires is at least 28000.
b)
Hypothesis:
H0 : mu = 5.5
Ha : mu not equal to 5.5
Test statistic:
x = 5.35 , s = 0.48 , n = 45
t = ( x - mean) / ( s/sqrt(n))
= ( 5.35 - 5.5)/( 0.48/ sqrt(45))
= -2.096
P value is calculated using t = -2.096 , df = 44
p value = .041868.
we fail to reject the null hypothesis. because p value is greater than 0.01 significance level.
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