Question

PLEASE SHOW THE CALCULATOR TI84 WAY OF DOING THIS. OR SHOW WORK

Each year the US Environmental Protection Agency (EPA) releases fuel economy data on cars manufactured in that year. Below are summary statistics on fuel efficiency (in miles/gallon) from random samples of cars with manual and automatic transmissions manufactured in 2012. Do these data provide strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage? Assume that conditions for inference are satisfied. City MPG, Automatic City MPG, Manual 19.85 4.51 26 16.12 3.58 26 Mean SD 35 25 automatic manual City MPG The h for this test are: O Ho: μautomatic- Lmanual Ha-Hautomatic sumama! Ha: Hautomatic Hmanual Ho: μautomati.- ¡manual The test statistic is: The p-value is (please round to two decimal places) (please round to four decimal places)

Answer 1

Your null and alternative hypothesis is correct let's find the test statistics and p-value using TI-84 calculator.

Click on STAT ------>TESTS----->2-SampTTest -------> Stats ------> Enter values ------>

$\bar{x1}$ : 16.12

Sx1: 3.58

n1: 26

$\bar{x2}$: 19.85

Sx2: 4.51

n2: 26

$\mu1:\neq \mu2$

Pooled: Yes

Calculate

We get

Test statistic = -3.30

P-value = 0.0018

P-value < 0.05 we reject null hypothesis.