A prototype from a hybrid vehicle manufacturer claims to get 50 miles per gallon (MPG). The manufacturer selects 14 prototypes from their fleet and drives the vehicles for fuel efficiency. The sample mean fuel efficiency for this sample was 53.3MPG and a standard deviation of 5.2MPG. Conduct a hypothesis test for the sample value at the α=0.05. What is the T-calculated value given the data? Report your answer to two decimal places and appropriate rounding.
To conduct a hypothesis test, we need to set up the null and alternative hypotheses:
Null hypothesis (H₀): The population mean fuel efficiency is equal to 50 MPG.
Alternative hypothesis (H₁): The population mean fuel efficiency is different from 50 MPG.
The next step is to calculate the T-calculated value using the formula:
T = (sample mean - hypothesized mean) / (sample standard deviation / √sample size)
Given that the sample mean is 53.3 MPG, the hypothesized mean is 50 MPG, the sample standard deviation is 5.2 MPG, and the sample size is 14, we can plug these values into the formula:
T = (53.3 - 50) / (5.2 / √14)
Calculating this expression, we get:
T = 3.3 / (5.2 / √14)
Now, we can evaluate this expression:
T ≈ 3.3 / 1.392
T ≈ 2.37 (rounded to two decimal places)
Therefore, the T-calculated value given the data is approximately 2.37.