A car company says that the mean gas mileage for its luxury sedan is 21 mpg. You believe the mean gas mileage is lower than this and find that a random sample of 5 cars has a mean gas mileage of 19 mpg and a sample standard deviation of 4 mpg. Assume the gas mileage of all of the company’s luxury sedans is normally distributed. At α = 0.10, use a t-test to assert the validity of the company’s claim.

Question

The test statistic is:
Question 19 options:

1.12

-1.12

2.92

-2.92

Answer 1

To test the validity of the company's claim, we can use a one-sample t-test. The test statistic for a one-sample t-test is calculated as:

t = (sample mean - population mean) / (sample standard deviation / √sample size)

Plugging in the given values:

sample mean = 19 mpg
population mean = 21 mpg
sample standard deviation = 4 mpg
sample size = 5

t = (19 - 21) / (4 / √5)
t = -2 / (4 / √5)
t = -2 / (4 / 2.236)
t = -2 / 1.788
t = -1.118

Rounding to two decimal places, the test statistic is -1.12. Therefore, the correct option is -1.12.