Answer to Question #181309 in Statistics and Probability for Cream

Question

According to the World Health Organization’s statistics published in 2018, the lifespan of a person 

in the Philippines is 67 years old. A random sample of 25 obituary notices in the Philippine Daily 

Inquirer has an average mean of 60 years old with a standard deviation of 19 years. If the life 

span in the Philippines is normally distributed, does this information indicate that the population 

mean life span of Filipinos is less than 67 years old? Use 5% level of significance.

Answer 1

Let $\mu$ be the the population mean life span of the Filipinos

$\mu_0=67$ years, the lifespan of a person in the Philippines.

$\bar{X}=60$ years, the lifespan established by the Philippine Daily Inquirer from a sample of 25 ($n=25$ ) with a standard deviation, $s=19$ years.

To establish whether this information indicate that the population mean lifespan of Filipinos ($\mu$)  is less than 67 years old, we proceed as follows.

Step 1: We specify the null and alternative hypotheses. He we use the notation $\mu$ already introduced.

$H_0: \mu=67$ $\text{ vs } H_a: \mu< 67$

Step 2: Compute the test statistic.

$z=\frac{\bar{X}-\mu_0}{\frac{s}{\sqrt{n}}}=\frac{60-67}{\frac{19}{\sqrt{25}}}=\frac{-7}{3.8}=-1.842$

Step 3: Find the p-value.

From the standard normal table, the area below -1.842 is given by 0.03288 which is the p-value in this case.

Step 4: Make a conclusion about the hypotheses at $\alpha=0.05$.

Since p-value=0.03288<0.05, the null hypothesis is rejected implying that result is statistically significant.

Step 5: Report the conclusion in the context of the question.

Since the null hypothesis is rejected, we can conclude that the population mean lifespan of Filipinos is less than 67 years.