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Rewa Delta Union Rugby CEO has become concerned about the slow pace of the rugby games played in the current union rugby, fearing that it will lower the spectator attendance. The CEO meets with the union rugby managers and referees and discusses guidelines for speeding up and making the games more interesting and lively. Before the meeting, the mean duration of the 15sided rugby game time was 3 hours, 5 minutes, that is, 185 minutes. This includes all the breaks and injury times during the game. A random sample of 36 of the 15-sided rugby games after the meeting showed a mean of 179 minutes with a standard deviation of 12 minutes. Testing at the 1% significance level, can you conclude that the mean duration of 15-sided union rugby games has decreased after the meeting?

Respuesta :

Answer:

We conclude that the mean duration of 15-sided union rugby games has decreased after the meeting.

Step-by-step explanation:

We are given that Before the meeting, the mean duration of the 15-sided rugby game time was 3 hours, 5 minutes, that is, 185 minutes.

A random sample of 36 of the 15-sided rugby games after the meeting showed a mean of 179 minutes with a standard deviation of 12 minutes.

Let [tex]\mu[/tex] = mean duration of 15-sided union rugby games after the meeting.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 185 minutes      {means that the mean duration of 15-sided union rugby games has increased or remained same after the meeting}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 185 minutes     {means that the mean duration of 15-sided union rugby games has decreased after the meeting}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

                            T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean duration of 15-sided union rugby games = 179 min

            s = sample standard deviation = 12 minutes

            n = sample of 15-sided rugby games = 36

So, the test statistics  =  [tex]\frac{179-185}{\frac{12}{\sqrt{36} } }[/tex]  ~ [tex]t_3_5[/tex]

                                       =  -3

The value of t test statistics is -3.

Now, at 1% significance level the t table gives critical value of -2.437 at 35 degree of freedom for left-tailed test.

Since our test statistic is less than the critical value of t as -3 < -2.437, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean duration of 15-sided union rugby games has decreased after the meeting.

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