Question

An obstetrician wants to know whether or not the proportions of children born on each day of the week are the same. She randomly selects 500 birth records and obtains the data shown in table. Is there reason to believe that the day on which a child is born occurs with equal frequency at the alpha= 0.01.

	Sunday	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday
Observed count (O)	46	76	83	81	81	80	53

PLEASE FOLLOW THE STEPS BELOW:

• You need formulate null hypothesis and alternative hypothesis
• Select alpha
• Compute expected count
• Compute chi-square
• Find p-value
• Make a decision.

Answer 1

Null and Alternative Hypotheses

Select alpha

α = 0.01

Compute expected count

Compute chi-square

Chi-square = 19.568

Find p-value

The number of degrees of freedom is df = 7 - 1 = 6

χ² = 19.568

P-value corresponding to χ² = 19.568 and df = 6 is 0.0033 (Obtained using online calculator. Screenshot attached)

Make a decision

Since p-value (0.0033) < α = 0.01, we reject null hypothesis.

Therefore, there is sufficient evidence to reject the claim that the day on which a child is born occurs with equal frequency at the alpha = 0.01.