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Sedaia [141]
2 years ago
11

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?
Mathematics
1 answer:
kkurt [141]2 years ago
5 0

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

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