Conducting a Chi-Square Test for Goodness of Fit — Quiz
Question 1 • Statistics
A researcher would like to investigate if the distribution of the number of babies born is uniform across the days of the week. To investigate, the researcher selects a random sample of 350 babies and records on which day of the week they were born. He finds that 28 babies were born on Sundays, 65 on Mondays, 48 on Tuesdays, 56 on Wednesdays, 45 on Thursdays, 62 on Fridays, and 46 on Saturdays. The researcher would like to know if there is convincing evidence that the distribution of births is uniform across the days of the week. What is the value of the chi-square test statistic and the cap p -value of this test? Use the chi-square distribution table.
Answer
A
chi squared is equal to 18 point 6 8 , cap p -value is between 0 point 0 0 2 5 and 0 point 0 0 5
B
chi squared is equal to 18 point 6 8 , cap p -value is between 0 point 0 0 5 and 0 point 0 1
C
chi squared is equal to 24 point 7 0 , cap p -value is between 0 point 0 0 0 5 and 0 point 0 0 1
D
chi squared is equal to 24 point 7 0 , cap p -value is less than 0 point 0 0 0 5
Explanation
If births are uniform across 7 days, the expected count is 350 ÷ 7 = 50 births per day. Adding the contributions (observed − expected)² ÷ expected gives χ² = 9.68 + 4.50 + 0.08 + 0.72 + 0.50 + 2.88 + 0.32 = 18.68. With 7 − 1 = 6 degrees of freedom, the chi-square table places this statistic between the upper-tail critical values for p = 0.005 and p = 0.0025. Thus the chi-square statistic is 18.68 and the p-value is between 0.0025 and 0.005, choice A.
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