Hypothesis Testing - Statistics

Hypothesis Testing Paper

Previously a group of friends compared the average temperature for the 15 days in each of the 2004 and 2005 Christmas holiday pubic school vacations to determine which holiday was colder. Secondary research retrieved from the National Oceanic and Atmospheric Administration's (NOAA) National Weather Service website provided climatic data on a daily basis for each day of the periods under investigation. Daily average temperature for each of the 15-day holiday vacation periods were gathered as two samples. The friends established a null hypothesis that the Christmas holiday vacation period of 2004 was colder than that of the 2005 Christmas holiday vacation period. After the completion of a five-step hypothesis test using a t-test, the null hypothesis was accepted. The acceptance of this null hypothesis led to further discussion on the comparison of the two periods.

The suggestion arose that perhaps the 2004 holiday vacation was colder in part due a higher occurrence of weather changes. The friends agreed that the arrival of colder winter weather always seemed to follow a period of increased winds. A new hypothesis that the colder 2004 Christmas vacation period was windier than that of 2005 was developed. The friends researched the wind speed of the holiday periods and implemented the five-step process for hypothesis testing.

Hypothesis

The average wind for the 15 days in 2004 Christmas holiday vacation is not equal to the average wind speed for 15 days of the 2005 Christmas holiday vacation.

After secondary research from the National Weather Service (2006), the mean wind speed for the 2004 Christmas holiday vacation is calculated at approximately 6.6 mph and serves as the population mean wind speed in the test statistic.

The null and alternate hypotheses are stated:

H0: 

H1:

The result of this hypotheses test will allow the friends to determine if the days of the 2004 holiday vacation period were not only colder, which was accepted in the previous hypothesis test, but were also were windier.

Determine the level of significance

The selection of a level of significance is .01 as an effort to reduce the chance committing errors. A Type I error occurs is the null hypothesis (Ho) is rejected when it is true. A Type II error is committed when the null hypothesis (Ho) is accepted when it is false.

Select a test statistic

The use of the T-statistic is appropriate as there are two separate samples comprised of fifteen days each. The test is a two-tailed test because H1 does not state a direction.

The calculated value of t is 2.323

Formulate