Question

A swine producer wants to know if the average weight of his pigs is different from the breed average of 230 lb. He selects a random sample of 16 weights from pigs in his herd and calculates a sample mean of 220 lb and a sample standard deviation of 25 lb. Assume that he wants to detect departure from 230 lb in either direction and that he uses a significance level of 0.10. Calculate the value of the test statistic needed to test the null hypothesis.

Answer 1

Answer: t= -1.60

Explanation:

Let $\mu$ be the population mean weight of pigs.

As per given , we have

$H_0:\mu=230$

$H_0:\mu\neq230$

Sample size : n= 16

Sample mean =$\overline{x}=220\ lb$

Sample standard deviation : $s=25\ lb$

Since the population standard deviation is not known so the test is a t-test.

Test statistic for population mean : $t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}$

$t=\dfrac{220-230}{\dfrac{25}{\sqrt{16}}}$ (Substitute all the values.)

$t=\dfrac{-10}{\dfrac{25}{4}}$

$t=\dfrac{-40}{25}=-1.60$

Hence, the value of the test statistic needed to test the null hypothesis : t= -1.60