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
= <em><u>mean duration of 15-sided union rugby games after the meeting.</u></em>
So, Null Hypothesis,
:
185 minutes {means that the mean duration of 15-sided union rugby games has increased or remained same after the meeting}
Alternate Hypothesis,
:
< 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 <u>One-sample t test statistics</u> as we don't know about the population standard deviation;
T.S. =
~ ![t_n_-_1](https://tex.z-dn.net/?f=t_n_-_1)
where,
= 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, <u><em>the test statistics</em></u> =
~ ![t_3_5](https://tex.z-dn.net/?f=t_3_5)
= -3
The value of t test statistics is -3.
<u>Now, at 1% significance level the t table gives critical value of -2.437 at 35 degree of freedom for left-tailed test.</u>
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 <u>we reject our null hypothesis</u>.
Therefore, we conclude that the mean duration of 15-sided union rugby games has decreased after the meeting.