Question

Scientists believe that ave. lifespan of US population is 75 years, with standard deviation of 6 years. But a person differed, and to prove his claim he collected life data from a sample of 40 people.

Write the null hypothesis and alternative hypothesis?
Which distribution he should use, t- distribution/ Z- distribution? Show reason for your answer.

Answer 1

$\small \mu_0 = 75$
$\small \\n = 40 \\\sigma = 6$
We are interested in testing the hypothesis
$\small \\Null\;Hypothesis --> H_0: \mu = \mu_0 \\Alternate\;Hypothesis --> H_1: \mu \ne \mu_0$

$\small \\Null\;Hypothesis --> H_0: \mu = 75 \\Alternate\;Hypothesis --> H_1: \mu \ne 75$

We will use z-distribution since number of samples is more than 30