Question

On a can of sardines it is written that the can contains 10 sardines. You open up 100 cans and find the average is 9.75 sardines with a standard deviation of 1.
What is the test statistic in a test of the null hypothesis that the population average is 10?

Answer 1

Answer: $t= -2.5$

Step-by-step explanation:

By considering the given statements :

Null hypothesis : $\mu=10$

Alternative hypothesis : $\mu\neq10$           ( opposite of null hypothesis.)

As per given , we have

Sample size : n= 100

Sample mean : $\overline{x}=9.75$

Sample standard deviations : $s=1$

Since population standard deviation is unknown , so we will perform t-test.

Formula for test statistic ( for population mean):

$t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}\\\\=\dfrac{9.75-10}{\dfrac{1}{\sqrt{100}}}\\\\=\dfrac{-0.25}{\dfrac{1}{10}}=-0.25\times10=-2.5$

Hence, the required test statistic : $t= -2.5$