Question

please help with parts a - c! thnks

pelase check roundings.

If there is no seasonal effect on human births, we would expect equal numbers of children to be bom in each season (winter, spring summer and foll) A student takes a census of her statistics class and finds that of the 120 students in the class, 25 were born in winter, 36 in spring, 31 in summer, and 28 infall She wonders of the excess in the spring is an indication that births are not uniform throughout the year. Complete parts a through c below a) Compute the standarduod residual for each season Standardred Residual Winter Spring Summer Fall (Round to three decimal places as needed)

Answer 1

Sol:

a).

observed frequencey, O	expected proportion	expected frequency,E	(O-E)	residual = (O-E)/√E
25	0.250	30.00	-5.00	-0.9128
36	0.250	30.00	6.00	1.095
31	0.250	30.00	1.00	0.1825
28	0.250	30.00	-2.00	-0.3651

b).

The standardized residuals are Z-scores and not particularly large because they are between - 2 and 2

option " a " is correct.

c).

Ho : Births are distributed uniformly across the seasons.

HA : Births are not distributed uniformly across the seasons

option " c " is correct.

d).

Critical value =    7.81

Since the test stastistic is " less than " the critical value. " fail to reject Ho "   Because of this conclusion " some of " the standardized residuals should be expected to be large in magnitude.

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