Question 1182532
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Add up the data values to get
5.95+6.10+5.98+6.01+6.25+5.85+5.91+6.05+5.88+5.91 = 59.89


Then divide that sum over n = 10
xbar = (sum of values)/n
xbar = (59.89)/10
xbar = 5.989
this is the sample mean


We're given sigma = 0.3 which is the population standard deviation. Because we know this value, we'll use the standard normal Z distribution.


Hypothesis 
H0: mu = 6
H1: {{{mu <> 6}}}
So either mu is 6 (null) or it's not 6 (alternative). The claim is in the null.
The alternative hypothesis tells us we have a two tailed test.


Test statistic:
z = (xbar - mu)/(sigma/sqrt(n))
z = (5.989 - 6)/(0.3/sqrt(10))
z = -0.11595018087283
z = -0.12


Now you have a few options at this point to find the p-value. One path is to use a table of values. Another is to use a graphing calculator or computer software.


If you go with the software option, then you can use something like this
<a href = "https://www.davidmlane.com/hyperstat/z_table.html">https://www.davidmlane.com/hyperstat/z_table.html</a>


Leave the "Area from a value" radio button as it is. Also, leave the "Mean" and "SD" boxes as 0 and 1 respectively. 


Then click on the "below" radio button. In the box next to it, type in -0.12 and hit "recalculate"
The result 0.4522 should pop up
<img width="35%" src = "https://i.imgur.com/gNqkbuu.png">


This represents P(z < -0.12) = 0.4522 approximately.
It's the approximate area under the Z curve that's to the left of -0.12


Double this value to get 2*0.4522 = 0.9044
This is the approximate p-value for the two tailed test. 


This is a very large p-value and it means we effectively fail to reject the null regardless of what alpha is.


The rule is:
If the p-value is smaller than alpha, then you reject the null. 
One way to remember is the phrase "if the p-value is low, then the null must go"


Conclusion:
We failed to reject the null, so we must conclude that mu = 6. Therefore, the average bottle contains 6 ounces of medicine. 
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