Question

An industrial supplier has shipped a truckload of teflon lubricant cartridges to an aerospace customer. The customer has been assured that the mean weight of these cartridges is in excess of the 12 ounces printed on each cartridge. To check this claim, a sample of n = 23 cartridges are randomly selected from the shipment and carefully weighed. Summary statistics for the sample are: x = 12.18 ounces, s = .23 ounce. To determine whether the supplier's claim is true, consider the test, H0: µ = 12 vs. Ha: µ > 12, where µ is the true mean weight of the cartridges. Calculate the value of the test statistic.

A) 0.783 B) 3.753 C) 18.000 D) 1.800

Answer 1

SOLUTION:

From given data,

An industrial supplier has shipped a truckload of teflon lubricant cartridges to an aerospace customer. The customer has been assured that the mean weight of these cartridges is in excess of the 12 ounces printed on each cartridge. To check this claim, a sample of n = 23 cartridges are randomly selected from the shipment and carefully weighed. Summary statistics for the sample are: x = 12.18 ounces, s = .23 ounce. To determine whether the supplier's claim is true, consider the test, H0: µ = 12 vs. Ha: µ > 12, where µ is the true mean weight of the cartridges. Calculate the value of the test statistic.

We have,

x = 12.18

n = 23

s = 0.23

Test hypothesis is:

Null hypothesis : H₀: µ = 12

Alternative hypothesis : H_a: µ > 12

Calculate the value of the test statistic.

Where,

is unknown so we consider t-dist

Test statistic = t = (x - µ) / (s / sqrt(n))

t = (12.18 - 12) / (0.23 / sqrt(23))

t = 0.18 / (0.23 / sqrt(23))

t = 0.18 / (0.23 / sqrt(23))

t = 3.753

Answer : option (B) is correct