Question

There are 218 first graders in an elementary school. Of these first graders, 86 are boys and 132 are girls. School wide, there are 753 boys and 1063 girls. The principal would like to know if the gender ratio in first grade reflects the gender ratio school wide.

a. identify the hypothesis

b. what are the degrees of freedom

c. complete this table in SPSS and paste the output below to replace it: (how do you set this up in SPSS)
Men Women

No. observed No. expected No. observed No. expected

d. calculate X² in SPSS and paste the output below

e. can you reject the null hypothesis at a=.05? Explain why or why not

Answer 1

When we go to enter our data in SPSS, we will need to create three new variables: gender , type , and a frequency variable (let's name it "frequency "). After entering the data, your Data View window should look like this:

Now we need to weight the cases with respect to Freq. Click Data > Weight Cases.

Click Weight cases by, then double-click Freq to move it to the Frequency Variable field. Click OK.

Now we can run our crosstab and verify your friend's results. Click Analyze > Descriptive Statistics > Crosstabs.

When the Crosstabs window opens, select the variable gender in the left column and move it to the Row(s)field using the first arrow button, then select variable type in the left column and transfer it to the Column(s) field using the second arrow button. Doing this will reproduce the 3x2 table that your friend made.

To produce a Chi-square test of independence, click Statistics. This will open the Crosstabs: Statistics window. Select the Chi-square check box in the upper left-hand corner, then click Continue

degree of freedom = 1

X² = 0.326

p-value = 0.568

hence we fail to reject the null hypothesis