Question

The earth's temperature can be measured using ground-based sensoring which is accurate but tedious, or infrared-sensoring which appears to introduce a bias into the temperature readings—that is, the average temperature reading may not be equal to the average obtained by ground-based sensoring. To determine the bias, readings were obtained at five different locations using both ground- and air-based temperature sensors. The readings (in degrees Celsius) are listed here.

Location	Ground	Air
1	46.8	47.5
2	45.5	48.3
3	36.2	37.7
4	31.1	32.9
5	24.6	26.0

State the test statistic. (Round your answer to three decimal places.)

t =

State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)

t	>
t	<

Estimate the difference in mean temperatures (in degrees Celsius) between ground- and air-based sensors using a 95% confidence interval. (Use μ_ground − μ_air. Round your answers to three decimal places.)

? °C to ? °C

How many paired observations are required to estimate the difference between mean temperatures for ground- versus air-based sensors correct to within 0.2°C, with probability approximately equal to 0.95? (Base your margin of error on a z critical value. Round your answer up to the nearest whole number.)

? paired observations

Answer 1

from above:

test statistic t = -4.803

t> 2.776

t< -2.776

for 95% CI; and 4 degree of freedom, value of t=			2.776
therefore confidence interval=sample mean -/+ t*std error
margin of errror          =t*std error=		0.948
lower confidence limit                     =		-2.5881
upper confidence limit                    =		-0.6919
from above 95% confidence interval for population mean =(-2.588 to -0.692)

c)

	for95% CI crtiical Z          =	1.960
	standard deviation σ=	0.764
	margin of error E =	0.2
required sample size n=(zσ/E)2                  =		56