Question

22a. Dr. Suzan Heverling claims that the number of births by day of week is not uniformly distributed. To test this claim you randomly select 700 births from a recent year and record the day of week on which each takes place. The table below shows the results. At a 10% significance level test the doctor’s claim.

DAY FREQUENCY

Sun 68

Mon 108

Tue 115

Wed 113

Thu 111

Fri 108

Sat 77

b. Two out of every five college graduates find a job in their field of study. If Anchorage, Alaska has 1500 college graduates this semester; find the mean variance and standard deviation of college graduates that did not find a job in their field of study.

Answer 1

(a) The hypothesis being tested is:

H₀: The number of births by day of week is uniformly distributed

H_a: The number of births by day of week is not uniformly distributed

observed	expected	O - E	(O - E)² / E
68	100.000	-32.000	10.240
108	100.000	8.000	0.640
115	100.000	15.000	2.250
113	100.000	13.000	1.690
111	100.000	11.000	1.210
108	100.000	8.000	0.640
77	100.000	-23.000	5.290
700	700.000	0.000	21.960
21.96	chi-square
6	df
.0012	p-value

The test statistic is 21.96.

The p-value is 0.0012.

Since the p-value (0.0012) is less than the significance level (0.10), we can reject the null hypothesis.

Therefore, we can conclude that the number of births by day of week is not uniformly distributed.

(b) p = 3/5 = 0.6

n = 1500

Mean = 0.6*1500 = 900

Varaince = 1500*0.6*0.4 = 360

Standard deviation = 1500*0.6*0.4 = 18.97

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