Question

Fach 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 a random sample of cars with manual transmissions and a random sample of cars with automatic transmissions manufactured in 2012. Assume that conditions for inference are satisfied City MPG Automatic Manual 16.12 19.85 3.58 4.51 Mean SD automatic manual City MPG (a) Compute the standard error (SE) of the difference of the two means. (b) Find the 90% confidence interval for the difference of the two means. (c) Find the 95% confidence interval for the difference of the two means. (d) Interpret in words what your answers to parts (b) or (c) mean.

Answer 1

a)

$12 SE = V1 + n2

  

(3.58) (4.51) - 06 十二

-1.1293

b)

(%+) 醒 -

  

(3: 31 (4)

= 47

At 90% confidence level, the critical value is t^* = 1.678

The 90% confidence interval is

() +/- t^* * SE

c1 – T2

= (16.12 - 19.85) +/- 1.678 * 1.1293

= -3.73 +/- 1.895

= -5.625, -1.835

c) At 95% confidence level, the critical value is t^* = 2.012

The 95% confidence interval is

() +/- t^* * SE

c1 – T2

= (16.12 - 19.85) +/- 2.012 * 1.1293

= -3.73 +/- 2.272

= -6.002, -1.458

d) We are 90% confidence that the difference between the true population means of fuel efficiency between the cars with automatic transmission and manual transmission lies within the confidence limits between -5.625 and -1.835.

We are 95% confidence that the difference between the true population means of fuel efficiency between the cars with automatic transmission and manual transmission lies within the confidence limits between -6.002 and -1.458.