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 45.3 47.9

3 36.2 37.7

4 30.9 32.9

5 24.6 26.0

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

t =  

b. 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	<

c. 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

d. 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

a) = (-0.7 + (-2.6) + (-1.5) + (-2) + (-1.4))/5 = -1.64

sd = sqrt(((-0.7 + 1.64)^2 + (-2.6 + 1.64)^2 + (-1.5 + 1.64)^2 + (-2 + 1.64)^2 + (-1.4 + 1.64)^2)/4) = 0.7092

The test statistic is

b) df = 5 - 1 = 4

At alpha = 0.05, the critical values are +/- t0.025,4 = +/- 2.777

c) At 95% confidence level, the critical value is t* = 2.777

The 95% confidence interval is

d) At 95% confidence level, the critical value is z* = 1.96

Margin of error = 0.2