Question

1. A consumer organization wants to estimate the actual tread wear index of a brand name of tires that claims​ "graded 250​" on the sidewall of the tire. A random sample of n=25 indicates a sample mean tread wear index of 238.8 and a sample standard deviation of 23.4. Complete parts​ (a) through​ (c).

a. Assuming that the population of tread wear indexes is normally​ distributed, construct a 90% confidence interval estimate of the population mean tread wear index for tires produced by this manufacturer under this brand name.

b..	Do you think that the consumer organization should accuse the manufacturer of producing tires that do not meet the perfomance information on the sidewall of the​ tire? Explain.

A.​Yes, because a grade of 250 is in the interval.

B. Yes because a grade of 250 is not in the interval.

C.​No, because a grade of 250 is not in the interval.

D. No because a grade of 250 is in the interval.

c.	Explain why an observed tread wear index of 247 for a particular tire is not​ unusual, even though it is outside the confidence interval developed in​ (a).

A.It is not unusual because it is only 0.35 standard deviations above the sample mean.

B. It is not unusual because it is actually in the confidence interval.

C.It is not unusual because it is just outside the confidence interval.

D.It is not unusual because it is only 0.01 standard deviations above the confidence interval.

Answer 1

a).the given data are:-

sample mean ()=238.80

sample sd(s)= 23.40

sample size(n)=25

here as the sample sd is known we will do 1 sample t test for mean.

degrees of freedom = (n-1) =(25-1) = 24

t critical value for 90% confidence level,df = 24, both tailed test be:-

[ from t distribution table]

the 90% confidence interval estimate of the population mean tread wear index for tires produced by this manufacturer under this brand name be:-

b).the correct option be:-

​No, because a grade of 250 is not in the interval.(C)

[ i think that the consumer organization should not accuse the manufacturer of producing tires that do not meet the performance information on the sidewall of the​ tire because the value 250 is outside the 90% confidence interval]

c).the correct option be:-

It is not unusual because it is just outside the confidence interval. (C)

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