# Sample Mean and Standard Deviation affects results to support reject Null Hypothesis

#### Stats_Beginner

##### New Member
Hi All,

I'm pretty new to Hypothesis Testing and I've come across a question I'm not sure of and was hoping someone could explain it.

Suppose we wish to test H0: µ = 15 , HA: µ ≠15. Which of the following possible sample results give the most evidence to support HA?

And the options are...

Sample mean = 19, sample standard deviation = 2

Sample mean = 12, sample standard deviation = 3

Sample mean = 17, sample standard deviation = 2

Sample mean = 13, sample standard deviation = 4

Sample mean = 11, sample standard deviation = 8

When I was researching this I found notes that stated if the sample statistic is far enough away from the hypothesised value then we can conclude that the Null Hypothesis is most likely false. So I was thinking the option with Sample Mean = 11 and sample standard deviation = 8 would be the best answer. However, I'm wondering if there is another theory behind it and I need to take the standard deviation into account.

Any help/advice is appreciated.

Thanks

#### Miner

##### TS Contributor
Re: Sample Mean and Standard Deviation affects results to support reject Null Hypothe

You need a 1-sample t-test. Here is a link to the formula.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Re: Sample Mean and Standard Deviation affects results to support reject Null Hypothe

What number is the furtherest away from the comparison value and has the smallest standard deviation? The key here is the standard deviation term once you get that a number further away is less likely to be equal to a value. Lastly, this is all assuming that all of the samples are equal in size.