Question

Q1. Historically, all matches in a tennis tournament used to have an average duration of
85.5 minutes and a standard deviation of 10.5 minutes. A researcher anticipates that these
have changed now. A sample of 36 match duration times are selected. The mean duration
time for selected matches is 89.5 minutes and standard deviation of duration of selected
matches is 8 minutes. Consider the following questions. [1+4+2+1+4+2 = 14 points]
(a) Suppose the researcher wants to test, at 5% level, the claim that the recent matches in
that tournament has different durations, on an average, compared to the past.
(i) Write it as ToH problem by describing ?! and ?" using mathematical notation for the
parameter of interest in the context of the problem.
(ii) Determine CR and conclude appropriately.
(iii) Now, solve the same problem by finding the p-value and show that you reach the same
conclusion as in Part (ii)

Answer 1

I)

ii) At alpha = 0.05, the critical values are +/- z0.025 = +/- 1.96

The test statistic is

  

  

Since the test statistic value is greater than the positive critical value(2.29 > 1.96), so we should reject the null hypothesis.

At 0.05 significance level, there is sufficient evidence to support the claim that the recent matches in that tournament has different durations, on average compared to the past.

iii) P-value = 2 * P(Z > 2.29)

= 2 * (1 - P(Z < 2.29))

= 2 * (1 - 0.9890)

= 0.0220

Since the P-value is less than the signifince level, so we should reject the null hypothesis.

At 0.05 significance level, there is sufficient evidence to support the claim that the recent matches in that tournament has different durations, on average compared to the past.