Question

Randomly selected birth records were obtained, and categorized as isted in the table to the right. Use a 0.01 significance level to test the reasonable claim that births occur with equal frequency on the different days of the week. How might the apparent lower frequencies on Saturday and Sunday be explained? Sun Mon Tues Day Thurs Wed Fri Sat Number of Births 38 55 59 55 57 57 47 Determine the null and alternative hypomesos. 0 Ho H Calculate the tout statistic, x? - (Round to three decimal places as needed.) Calculate the P-value Palue - Round to four decimal places as needed) What is the conclusion for is hypothesis test? O A Fail to roject. There is insufficient evidence to warrant rejection of the claim that births occur with equal frequency on the different days of the week. OB Fail to reject Ho. There is sufficient evidence to warrant rejection of the claim that births occur with equal frequency on the different days of the week OC. Reject Ho. There is sufficient evidence to warrant rejection of the claim that births occur with equal frequency on the different days of the week. OD. Reject Ho. There is insufficient evidence to warrant rejection of the claim that births occur with equal frequency on the different days of the week. How might the apparent lower frequencies on Saturday and Sunday be explained? O A. Induced or Caesarean section births are scheduled during the week whenever possible OB. Induced or Caesarean-section births are scheduled on weekends whenever possible.

Answer 1

CHI - SQUARE GOODNESS OF fit TEST : Test Statistic given by X² E. (fi-ei)? ei Comedie Obseared frequency fi : ei: Expected frequency Chi-square distribution follows (n-1) df. NOW Null same typothesis on the week.. (Ho): Bisths occurs with the frequency the different days of Alternative Hypothesis (Hi) : Hypothesis day different frequency of bister than the day Alleast one has a a in other Now, Under Null typothesis, Expected feequency Cei) = 38+55 +59+55 +54 +57447 52.57 Now CALCULATIONS:

A 00 C D 1 fi ei 2 (fi-ei) -14.57 2.43 6.43 38 55 59 3 4 E F (fi - ei)? (fi - ei) /eil 212.33 4.04 5.90 0.11 41.33 0.79 5.90 0.11 19.61 0.371 19.61 0.37 31.04 0.59 5 52.57 52.57 52.57 52.57 52.57 52.57 52.57 55 2.43 6 57 7 57 4.43 4.43 -5.57 8 47 9 SUM: 6.39

4.09 + 6.1 + 6.20 + 0.1 + 0.33 + 0-32 4 659 - 2 x = 6.39

the p-value : from given Puen Information, a = 0.01, degree of freedom and y = 6.39 PC Y > 6.39) = 0.381 p-value olue Now Since Our p-vall >0.01. so we fail to reject owe Ho. There is Insufficient Evidence to waosant ction Pon of the claim that bioths occue with on the equa the week. reject different days of be and Sunday 8 lower frequencies on on satwe Saturday Explained Induced or caesarean - section bioths are scheduled uri cohenever possible. by (A the week during