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In: Statistics and Probability

For each of the following research scenarios, give the appropriate sampling distribution (i.e., test statistic) and...

For each of the following research scenarios, give the appropriate sampling distribution (i.e., test statistic) and indicate the appropriate statistical procedure to test the null hypothesis, and state the most appropriate null and alternate hypotheses

A research group believes that changes in the annual extent of sea ice cover in the Beaufort Sea affects the mercury concentration in ringed seals that the people of Ulukhaktok (formerly known as Holman) NWT rely on as an important food source. They measured mercury concentrations in muscle samples from 20 male seals collected for the years 2013, 2014, 1015 and 1016 where ice cover differed considerably in each year.

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Expert Solution

The researcher wants to compare the mercury concentration in muscles when there is change in annual extent of sea ice cover in Beaufort Sea. So the respective hypothesis can be taken as:

Null hypothesis:Ho: there is no change in mean concentration of mercury in the given years due to change in extent of sea ice cover, or Miu(2013)=miu(2014)=miu(2015)=miu(2016)

Alternative hypothesis:H1: mean concentration of mercury differed considerably at least for one of the year.

The analysis of variance (ANOVA) for one way will be applied here in order to test the equality of different means. The test statistic will be F statistic. Since the sample size is 20 so degree of freedom for F distribution will be (4-1,20-4)=(3,16).

Now, find the sample mean for each year, and then the treatment sum of square by findingthe differenceof each mean from overallmean and then squaring their differences, error sum of square will be calculated by finding the difference of each of the values in a given year from their respective mean and summing their squares. The sum of treatment sum of square and error sum of square will give total sum of square. Now, divide the sum of squares by their degree of freedom to obtain mean sum of square. F statistic =Mean sum of square of treatment divided by mean sum of square error. This will give F calculated value, now get F tabulated value at (3,16) degree of freedom from F table. Compare F calculated with F tabulated, if F calculated is greater than F tabulated, reject Ho at alpha level of significance.

Thank you and please rate the answer.

orchestra answered 1 year ago
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