Worksheet 4 b- Analyzing categorical data The Chi-squared distribution using SPs

Question

Worksheet 4 b- Analyzing categorical data The Chi-squared distribution using SPss Singing crickets: In a study on the mating and courtship habits of crickets, field biologists gathered a set of data on crickets in a wildflower meadow. They recorded wing tip color and length of song for a set of 7o male crickets. In this exercise, we will be exploring the data on wingtip color. 1. open up the dataset labeled singing crickets How many cases in the dataset? Describe the data on wing tip color. Do you foresee any problems? there is red, As youll see, you11 need to recode the data into numeric codes. So, go ahead and outline the steps below, then recode your data. Use 1 for green, 2 for blue and 3 for okay, we are ready to start the analysis. What is the your first step in any data analysis? Hopefully, you've decided to produce a bar chart to show the relative frequencies of each class. Sketch your bar chart below

Explanation / Answer

Question 1

Answer:

Question for this hypothesis test is given as below:

Whether all three colours are equally distributed or not?

Question 2

Answer:

The null and alternative hypotheses are given as below:

H0: Three colours are equally distributed.

Ha: Three colours are not equally distributed.

Question 3

Answer:

For the given data, we observed that the data for the variable colour is a categorical variable. Here, we want to test whether the specific distribution with equal proportions for each colour fits to the given data or not. For checking this hypothesis we have to use the Chi square test for goodness of fit.

Question 4

Answer:

The given box or table gives us information about the observed frequencies and expected frequencies. The second table gives us the value of Chi square test statistic with degrees of freedom and p-value.

We are given

2 = 20.257

d.f. = 2

p = 0.000

Question 5

Answer:

= 0.05

p = 0.000

p < , so we reject the null hypothesis H0

Question 6

Conclusion:

We conclude that there is sufficient evidence that given three colours are not equally distributed.

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