Question

Directions: Read and answer each question carefully. For any hypothesis test, be sure to state your Ho and Ha, test statistic, p-value, and conclusion the words of the problem. For any confidence interval be sure to interpret the interval in the words of the problem. Round answers to the thousandths place.

Consider a small scale example, comparing how temperatures have changed in the US from1968 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. The locations are the same for both years. 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. Does the data provide evidence that the true mean temperature is different in 2008 than in 1968? Justify fully at the 5% significance level.

Answer 1

Answer:

Given,

Ho : u = 0

Ha : u != 0

consider,

test statistic t = (x - u)/(s/sqrt(n))

substitute values

= (1.1 - 0)/(4.9/sqrt(51))

= 1.6032

degree of freedom = n - 1 = 51-1 = 50

P value = 0.115234

= 0.1152

Here p value > alpha, so we reject Ho.

So we have sufficient evidence.