# 9.4, 9.5 Hypothesis Testing

# Problem 1

Jaidyn thinks that people living in a rural environment have a healthier lifestyle than other people. He thinks that the average lifespan in the USA is 77 years. A random sample of 14 obituaries from newspapers from rural towns in Massachusetts give [latex]\bar{x}[/latex] = 81*.*09 and *s *= 0*.*91. Does this sample provide evidence that people living in rural communities live longer than 77 years?

a. State the null and alternative hypotheses: (Type “mu” for the symbol *µ*, e.g. **mu **> **1 **for the mean is greater than 1, **mu **< **1 **for the mean is less than 1, **mu not = 1 **for the mean is not equal to 1)

*H*_{0}:

*H*_{a}:

b. Find the test statistic, *t *=

c. To a 10% level of significance, does this sample provide evidence that people living in rural communities live longer than 77 years. [Yes/No]

## Correct Answers

a. mu = 77; mu > 77

b. [latex]\frac{81.09-77}{\frac{0.91}{\sqrt{14}}}[/latex]

c. Yes