Answer to Question #210468 in Statistics and Probability for Janna

Question

Performance Task - Hypothesis Testing on Population Mean

Title: Mean Height of Local Adults

Directions: In a national survey by Food and Nutrition Research Institute of the Department of

Science and Technology on April 2014 to adult Filipinos (20 years old and older), the average

height of males is 163 cm with a standard deviation of 6 cm, and the average height of females

is 151.4 cm with a standard deviation of 5 cm. You are a local statistician and you are interested

to know if the average height of the adult males (or females) in your locality is different to the

national average height. Use the knowledge on Hypothesis Testing on Population Mean, and do

the following:

C. At 95% confidence, test the null hypothesis that there is no significant difference

between the national average height and the local average height.

Answer 1

I have not received the measurements; however, I will solve the questions using assumed figures

Assume that a random sample of 100 local males resulted in an average height of 165 cm.

$H0:\mu=163$

$Ha:\mu\ne163$

$\bar{X}=165$

$\mu=163$

$\sigma=6$

$n=100$

Since population standard deviation is known, z-score is used.

$Z=\frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt{n}}}$

$Z=\frac{165-163}{\frac{6}{\sqrt{109}}}=3.33$

Cv$=z_{0.025}=1.96$

Since the test statistic (3.33) is greater than the critical value (1.96), we reject the null hypothesis and conclude that the average local males height is significantly different from the average national male heights.