Question

Is there strong evidence of global warming? 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

Is there a relationship between the observations collected in 1968 and 2008? Or are the observations in the two groups independent? Explain

Write hypotheses for this research in symbols and in words.

Check the conditions required to complete this test.

Calculate the test statistic and find the p-value.

What do you conclude? Interpret your conclusion in context.

Based on the results of this hypothesis test, would you expect a confidence interval for the average difference between the temperature measurements from 1968 and 2008 to include 0? Explain your reasoning.

Calculate the 90%, 95%, 99% Confidence Interval. Is this result surprising based on your answer to the previous question? Why/Why not?

Answer 1

(a)

Here have have 51 paired observations. It is an example of depedent sample t test.

(b)

The hypotheses are:

Null hypothesesis, H0: There is no signficant difference between the temperatures.

Aternative hypothesesis, Ha: There is a signficant difference (positive) between the temperatures.

(c)

Here paired sample t test will be used. Since sample size is large so normality can be assumed.

That is condition for the test are fullfilled.

(d)

Given info;

So test statistics will be

Degree of freedom: df=n-1=51-1=50

The p-value is : 0.0579

(e)

Since p-value is greater than 0.05 so we fail to reject the null hypothesis.

That is we cannot conclude that there is evidence of temperature warming in the continental US.