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

Step-by-step explanation:

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

As per given , we have

`H_0:\mu=230`

`H_0:\mu\\eq230`

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=\frac{\overline{x}-\mu}{(s)/(√(n))}`

`t=(220-230)/((25)/(√(16)))` (Substitute all the values.)

`t=(-10)/((25)/(4))`

`t=(-40)/(25)=-1.60`

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