Let\'s assume the Average Speed of a Serve in Women\'s tennis is around 118mph,

Question

Let's assume the Average Speed of a Serve in Women's tennis is around 118mph, with a standard deviation of 12mph. We recruit 100 amateur tennis players to use a new method of serving. After 6 months we calcualte a group mean of 123mph.
A) Conduct the 6 steps of hypothesis testing to see if the amateur tennis players average a higher speed than the average using an alpha of 0.5.
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6.
B) What is the 95% confidence interval for the sample?
C) Compute the effect size and describe its strength.

Explanation / Answer

null hypothesis: mean =118

alternate hypothesis: mean >123

we will use one sample z test as population std deviation is known

std error of mean =std deviation/(n)1/2 =1.2

critical value for 0.05 level =1.6449

test stat z=(X-mean)/std error =(123-118)/std error =4.1667

p vlaue for above =0.0000

as p value is less then 0.05 level we rejct null hypothesis and accept that speed is higher then 118.

B)for 95% CI, z=1.96

hence confidence interval =sample mean -/+ z*Std error =120.648 ; 125.352

C)effect size =(123-118)/12 =5/12 =0.4167

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