Determine what statistical test should be used to analyze the data. Summarize al

Question

Determine what statistical test should be used to analyze the data.

Summarize all information used to determine the correct statistical test (e.g., number of groups, type of data collected, independent or repeated measures)

State what statistical test should be used (be specific).

Provide a sample size and critical values in relation to the hypothesis (Note that you have been provided all of the needed information to determine the critical value(s)) and determineany potential problems to watch out for, including an appropriate sample size to meet the assumptions of the statistical test .

Client Scenario: No Worries Cruise Line

                  No Worries Cruise Line has started receiving less customers, and they are starting to get worried as to what is happening. A corporate employee, Eddie, has been asked to look into the matter. Eddie gathered up all the contact information of everyone who went on one of their cruises for the last three years. In order to gauge differences in satisfaction, Eddie created a questionnaire, which he sent to everyone who had taken a cruise with them the last three years. He had them rate levels of happiness, relaxation, food/drink quality, and entertainment quality on scales of 1-10, with 10 being highest level. He gave anyone who completed the survey a 10.00 dollar Starbucks card. He got 3,000 responses, with 1,000 responses from each of the last three years. Eddie does not know how to statistically examine the data, so he asks you to consult him on how to examine the data. The key question that Eddie needs answered is how to determine if satisfaction levels have changed over these last few years.

Explanation / Answer

The test that needs to be conducted is based on the following observations:

We got responses regarding single factor : Satisfaction level

We got the data for 3 different groups: 3 years

In such a case: the best test that helps us compare the mean satsifaction level in the three year is Single factor ANOVA test

We specifically start with the null hypothesis: Mean satisfaction level is same for all the years

Alternate hypothesis would be: Mean satisfaction level is different for atleast any one year.

.

The appropriaate sample size can be : 50 responses from each year

It may be a random selection

this sample size is correct as per the condition that the sample size must be less than 10% of the population size

so since each year has 1000 responses, its 10% is 100

Thus the sample size < 100 is correct

So we get 50 people in each year, thus making the total Sample size as 150

.

For critical value calculation:

we need df for numerator = df N = number of groups -1 = 3-1 = 2

df for denominator = N - number of groups = 150-3 = 147

And let us consider the significance level = 0.05

Now we can refer the F table of find thr F critical value with the help of excel formula as shown below:

=FINV(0.05,2,147)

We get the F critical value as :

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