Question

In: Statistics and Probability

Freddie is working on his tennis serve. While practicing, he gets 15 out of 20 in...

Freddie is working on his tennis serve. While practicing, he gets 15 out of 20 in bounds (75% in bounds). Freddie wants to know if his long-run proportion of getting his serves in bounds in is greater than 50%.

a) Describe the parameter of interest in the context of this study. Also identify the symbol for this parameter.

b) What is the value of the observed statistic including the correct symbol? Identify the correct symbol we should use for this statistic.

c) Write out the null and alternative hypotheses for this study in words and also in symbols.

d) Use the One Proportion applet to generate 1000 simulated samples and find the p-value on the simulation applet. Copy and paste a screen shot of what you entered into the applet and also the resulting simulated distribution. Make sure that your screen shot shows your p-value and what you entered in the applet.

e) Calculate the value of the standardized statistic, and also identify the correct symbol. Show all work.

f) Write the literal interpretation of the p-value in terms of Freddy’s serves. (Hint: “If we assume ____ then the probability of ___ is ___.”) g) (3 points) Write the conclusion we should draw about Freddy’s serves. (Hint: “We have strong evidence ….” or “It is plausible that…” etc.)

Expert Solution

(a) The parameter of interest is the proportion of getting Freddie's tennis serves in bounds, p = 0.50.

(b) The value of the observed statistic, p̂ = 15/20 = 0.75.

(c) The hypothesis being tested is:

H₀: p = 0.5

H₀: Long-run proportion of getting Freddie's tennis serves in bounds in is 50%

H_a: p > 0.5

H_a: Long-run proportion of getting Freddie's tennis serves in bounds in is greater than 50%

(d) The output is:

The p-value is 0.3274.

(e) The test statistic, z = (p̂ - p)/√p(1-p)/n

z = (0.55 - 0.5)/√0.5(1-0.5)/20

z = 0.45

(f) If we assume that the null hypothesis is true, then the probability of getting the test statistic as extreme as possible is 0.3274.

(g) We do not have any evidence that the proportion of Freddie's tennis serves in bounds is greater than 50%.

orchestra answered 2 years ago

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