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KvngLij
16.12.2020 •
Mathematics
Can someone help me !
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Ответ:
We conclude that the younger group have a lower mean time in seconds than the older group.
Step-by-step explanation:
We are given that for 24 younger adults (21-36 years), the average time for navigation entry was 31.4 seconds versus 40 seconds for the 24 participants in the older group (55-75 years).
Standard deviations are not given, so we estimate the younger group at 0.99 seconds and the older group at 1.04 seconds.
We have to conduct a hypothesis test to see whether the younger group have a lower mean time in seconds than the older group.
Let
= population mean time for navigation entry for younger groups
SO, Null Hypothesis,
:
or
{means that the younger group have a mean time in seconds higher than or equal to the older group}
Alternate Hypothesis,
:
or
{means that the younger group have a lower mean time in seconds than the older group}
The test statistics that will be used here is Two-sample t test statistics as we don't know about the population standard deviations;
T.S. =
~ ![t__n__1+n_2-_2](/tpl/images/0586/9522/7d631.png)
where,
= sample average time for navigation entry for younger adults (21-36 years) = 31.4 seconds
Here,
=
= 1.015
So, test statistics =
~ ![t_4_6](/tpl/images/0586/9522/f0193.png)
= -29.35
So, at 0.05 level of significance, the t table gives critical value of -1.6792 at 46 degree of freedom for one-tailed test. Since our test statistics is way less than the critical value of t so we have sufficient evidence to reject null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the younger group have a lower mean time in seconds than the older group.