For any hypothesis test, be sure to state your Ho and Ha, test statistic, p-valu

Question

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 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. (Does the data provide evidence that the true mean temperature is greater in 2008 than in 1968?) Justify fully at the 5% significance level.

Explanation / Answer

The two measurements are independent. The measurements from 1968 do not in any way affect the measurements from 2008, or vice versa. Furthermore, knowing the outcomes of one set of measurements provides no useful information regarding the outcomes from the other set of measurements.

Secondly, the textbook states that sample observations are independent if the observations are from a simple random sample and consist of fewer than 10% of the population. I am going to assume that the population of locations from which the 51 locations were sampled is at least 510 locations.

H0: diff=0 There is no difference between average daily high temperatures on Jan 1, 1968 and Jan 1, 2008 (null hypothesis)

HA: diff>0 Average daily high temperatures on Jan 1, 2008 are higher than Jan 1, 1968 (alternative hypothesis)

I see this as a one-tailed test, because the research question is not concerned with testing for global cooling or warming, just global warming.

Since the p-value 0.0544 exceeds the value, I fail to reject the null hypothesis. The data does not provide strong evidence that the 2008 temperatures are greater than the 1968 temperatures, though it is pretty close.

0 lies in the interval thus null is accepted

Thus, There is no difference between average daily high temperatures on Jan 1, 1968 and Jan 1, 2008

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