Question

A sample of 9 days over the past six months showed that a dentist treated the following numbers of patients: 23, 26, 21, 19, 16, 22, 23, 19, and 25. If the number of patients seen per day is normally distributed, would an analysis of these sample data reject the hypothesis that the variance in the number of patients seen per day is equal to 10? Use a .10 level of significance. a. State the null and alternative hypotheses. H 0:02 equal to 10 not equal to 10 b. Calculate the value of the test statistic (to 2 decimals). 7.13

Answer 1

	Values ( X )	Σ ( Xi- X̅ )2
	23	2.0863
	26	19.7527
	21	0.3087
	19	6.5311
	16	30.8647
	22	0.1975
	23	2.0863
	19	6.5311
	25	11.8639
Total	194	80.2223

Mean X̅ = Σ Xi / n
X̅ = 194 / 9 = 21.5556
Sample Standard deviation S_X = √ ( (Xi - X̅ )² / n - 1 )
S_X = √ ( 80.2223 / 9 -1 ) = 3.1667

Test Statistic :-

χ² = ( ( 9-1 ) * 10.028 ) / 10
χ² = 8.02

x = ((n − 1)2)/04

Question 2

Test Statistic :-

f = 8.5 / 4
f = 2.13

f = S/S