Andrew thinks that people living in a rural environment have a healthier lifestyle than other people. he believes the average lifespan in the usa is 77 years. a random sample of 11 obituaries from newspapers from rural towns in idaho gives x¯=79.14 and s=2.48. does this sample provide evidence that people living in rural idaho communities live longer than 77 years? use a 10% level of significance.

Yes, it does.

Step-by-step explanation:

Since the data is approximately Normally distributed and the sample is less than 30, we will be using the Student's t Distribution.

: 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

TINV(0.2,10)

In OpenOffice Calc use

TINV(0.2;10)

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.

answer: y = -2.5x - 15

              (-6,0)

step-by-step explanation: