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.**

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....

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1.The sample mean is an unbiased estimator for
the population mean. This means:
The sample mean always equals the population mean.
The average sample mean, over all possible samples, equals the
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