Question

How would I explain the results of the chi-squared test below?

to someone who does not understand statistics

Use clear language and provide a complete answer.

Do You Work?

	Observed N	Expected N	Residual
Yes	16	10.0	6.0
No	4	10.0	-6.0
Total	20

Test Statistics

	Do you work?
Chi-Square	7,000
df	1
Asump. Sig.	.007

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: The observed values are in accordance with expeted values.

Alternative hypothesis: At least one of the proportions in the null hypothesis is false.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square goodness of fit test of the null hypothesis.

Analyze sample data. Applying the chi-square goodness of fit test to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = k - 1 = 2 - 1
D.F = 1
(E_i) = n * p_i


X² = 7.20

where DF is the degrees of freedom, k is the number of levels of the categorical variable, n is the number of observations in the sample, E_i is the expected frequency count for level i, O_i is the observed frequency count for level i, and X² is the chi-square test statistic.

The P-value is the probability that a chi-square statistic having 1 degrees of freedom is more extreme than 7.20.

We use the Chi-Square Distribution Calculator to find P(X² > 7.20) = 0.007.

Interpret results. Since the P-value (0.007) is less than the significance level (0.05), we cannot accept the null hypothesis.