Question

Let's consider a small scale example, comparing how temperatures have changed in the US from 1968 to 2008. The daily high temperature reading on January 1 was collected in 1968 and 2008 for 51 randomly selected locations in the continental US. Then the difference between the two readings (temperature in 2008 - temperature in 1968) was calculated for each of the 51 different locations. The average of these 51 values was 1.1 degrees with a standard deviation of 4.9 degrees. We are interested in determining whether these data provide strong evidence of temperature warming in the continental US. Calculate the confidence intervals for 90%,95%, 99%

Answer 1

Solution :

Given that mean x-bar = 1.1 , standard deviation s = 4.9 , n = 51

=> df = n - 1 = 50

=> For 90% confidence interval , t = 1.676

=> The 90% confidence interval of the mean is

=> x-bar +/- t*s/sqrt(n)

=> 1.1 +/- 1.676*4.9/sqrt(51)

=> (-0.0500 , 2.2500)

=> For 95% confidence interval , t = 2.009

=> The 95% confidence interval of the mean is

=> x-bar +/- t*s/sqrt(n)

=> 1.1 +/- 2.009*4.9/sqrt(51)

=> (-0.2784 , 2.4784)

=> For 99% confidence interval , t = 2.678

=> The 99% confidence interval of the mean is

=> x-bar +/- t*s/sqrt(n)

=> 1.1 +/- 2.678*4.9/sqrt(51)

=> (-0.7375 , 2.9375)