155k views
1 vote
A tire company guarantees that a particular brand of tire has a mean useful lifetime miles or more. A consumer testing agency sampled n = 10 tires on a test wheel that simulated conditions. The sample mean lifetimes (in thousands of miles) were as follows: 42 36 46 43 41 35 43 45 40 39 Construct a 98% CI for the mean lifetime of this particular brand of tire.

User Pptang
by
7.2k points

1 Answer

3 votes

Answer:

Explanation:

Number of sampled tyres = 10

To determine the mean, we will divide the total number of miles by the total number of tyres.

Mean, u = (42+36+46+43+41+35+43+45+40+39)/10 = 410/10 = 41

Standard deviation = √[summation(u - ub)^2]/n

ub = deviation from the mean, u

Summation(u - ub)^2] = (42-41)^2 + (36-41)^2 + (46-41)^2 +(43-41)^2 + (41-41)^2 + (35-41)^2 + (43-41)^2 + (45 -41)^2 + (40-41)^2 + (39-41)^2

= 1 + 25 + 25 + 4 + 0 + 36 + 4 + 16 + 1 + 4 = 116

Standard deviation = √116/10 = √11.6

= 3.41

We want to determine a 98% confidence interval for the mean mean lifetime of a particular brand of tire.

For a confidence level of 98%, the corresponding z value is 2.33. This is determined from the normal distribution table.

We will apply the formula

Confidence interval

= mean +/- z ×standard deviation/√n

It becomes

41 +/- 2.33 × 3.41/√10

= 41 +/- 2.33 × 10.78

= 41 +/- 25.11

The lower end of the confidence interval is 41 - 25.11 =15.89

The upper end of the confidence interval is 41 + 25.11 = 66.11

Therefore, with 98% confidence interval, the mean lifetime of a particular brand of tire is between 15.89 miles and 66.11 miles

User Sethfri
by
6.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.