Answer:
Yes, it does.
Step-by-step explanation:
<em>Since the data is approximately Normally distributed and the sample is less than 30, we will be using the Student's t Distribution.
</em>
: The life expectancy of people living in rural Idaho is 77 years
: The life expectancy of people living in rural Idaho is greater than 77 years.
So, this is a right-tailed test.
Our t-statistic is given by
where
= 79.14 is the mean of the sample
= 77 is the mean of the null hypothesis
s = 2.48 is the sample standard deviation
n = 11 is the sample size
Computing our t-statistic we get
Now, we obtain the critical upper value 
for a right-tailed test hypothesis corresponding to a 10% level of significance associated with the Student's t Distribution with 10 degrees of freedom (sample size-1). This is a value such that the area under the t distribution to the left of equals 10% = 0.01
We can do it either by looking up a table or a spreadsheet.
In Excel use
<em>TINV(0.2,10)
</em>
In OpenOffice Calc use
<em>TINV(0.2;10)
</em>
and we would get = 1.3722
Since our t-statistic is greater than we can reject the null hypothesis and say this sample provide evidence that people living in rural Idaho communities live longer than 77 years.
