Consider the following hypothesis test:

H0: ≤ 26
Ha: > 26

A sample of 40 provided a sample mean of 27.4. The population standard deviation is 6.

Compute the value of the test statistic (to 2 decimals).
What is the p-value (to 4 decimals)?

The p value can be founded with the following probability:

Step-by-step explanation:

Information given

represent the sample mean  

represent the population deviation

sample size  

represent the value to verify

z would represent the statistic

represent the p value

System of hypothesis

We want to check if the true mean for this case is higher than 26, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

The statistic is given by:

(1)  

Replacing the info we got:

The p value can be founded with the following probability:

5050

hope this !

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4