Question

assume the coach wanted a reliable estimate of her ability to play and allowed him to hit 10 rounds and took the average number of strokes of those 10 rounds. His rounds were: 72 74 69 72 71 72 71 72 72 73 Is there sufficient evidence to suggest that her true average is less than 73? Perform the 6 step hypothesis test at the alpha = .01 level of significance to find out! You may assume that her round scores come from a normal distribution. Be sure to include the appropriate confidence interval (the one that will always “agree” with your test) in your conclusion.

Answer 1

Xi	Xi-Xbar	(Xi-Xbar)^2
72	0.2	0.04
74	2.2	4.84
69	-2.8	7.84
72	0.2	0.04
71	-0.8	0.64
72	0.2	0.04
71	-0.8	0.64
72	0.2	0.04
72	0.2	0.04
73	1.2	1.44
718		15.6

Mean =

Sample variance =

s= 1.3165

Here the hypothesis is,

n= 10 (n<30) use t test

Test statistic,

t =

Degrees of freedom = n-1 = 9

|t₉| = 2.8823 .... calculated value

Table value = t_9,0.005 = 2.8214

Decision Rule - Calculate value = |t₉| > Table value = t_{9,0.005 ,}Reject H0 at 1% level of significance.

Or

P value = 0.009055 < 0.01

Reject H0 at 1% level of significance.

Conclusion : It is sufficient evidence that her true average is less than 73.

Confidence interval :