Question

New automobile tires, manufactured by a company in Lake Charles, are designed to provide a mean of at least 50,000 miles. Marissa Manuel, who is Production Manager, tested a random sample of tires and obtained the following descriptive statistics:

▪ Sample size: n =36 tires
▪ Sample mean: x̄ = 50,900 miles, and
▪ Sample standard deviation: s= 3,000 miles.

(1) Construct a 95% confidence interval for the mean length of life μ of all automobile tires.

(2) Test the alternate hypothesis that the mean length of life μ of all tires is greater than 50,000 miles.

Alternatives

Select one:

H₀: μ ≤ 50,000 H₁: μ > 50,000

H₀: μ ≥ 50,000 H₁: μ < 50,000

H₀: μ = 50,000 H₁: μ ≠ 50,000

H₀: μ ≠ 50,000 H₁: μ = 50,000

None of the other four

(ii) Test statistic

Select one:

z* = 1.60

z* = 1.645

z* = 2.20

z* = 1.96

None of the other four

(iii) p-value

Select one:

0.01

0.0227

0.0359

0.0718

None of the other four

(iv) What is the conclusion if the level of significance is α=0.05?

Select one:

Conclude H₀ that the mean length of life of all tires is less than 50,000 miles

Conclude H₀ that the mean length of life of all tires is greater than 50,000 miles

Conclude H₁ that the mean length of life of all tires is less than 50,000 miles

Conclude H₁ that the mean length of life of all tires is greater than 50,000 miles

None of the other four

Answer 1