Answer to Question #343419 in Statistics and Probability for Carla

Question

According to NSC statistics,the life expectancy of Filipino women is 70.1 years. Suppose a random sample of 30 women in town B yields a mean of 72.5 years with a population variance of 4.76 years, would you say that the life expextancy of the women in town B is greater than the average?Formulate the null and alternative hypothesis and in symbol.

Answer 1

The following null and alternative hypotheses need to be tested:

$H_0:\mu\le70.1$

$H_1:\mu>70.1$

This corresponds to a right-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

The rejection region for this right-tailed test is $R = \{z:z>z_c\}.$

The z-statistic is computed as follows:

$$z=\dfrac{\bar{x}-\mu}{\sigma/\sqrt{n}}=\dfrac{72.5-70.1}{4.76/\sqrt{30}}\approx2.7616$$