Answer:
Z Test = -3.87298
p= .0001
Then the results are significant at p values < 0.1
Step-by-step explanation:
To answer this question we have to consider some things.
1) The Mean of Population is given by this formula:
[tex]\mu =\frac{\sum X_{i}}{N}\; \mu=2.8[/tex]
The Population Standard Deviation is given by this formula:
[tex]\sigma =\frac{\sqrt{(x_{i}-\mu)^{2}}}{N}\: \sigma=0.4[/tex]
On the other hand, the Team buddies are a sample of this population, whose mean is:
[tex]\bar{x} = \frac{\sum x_{i} }{n}=2.3[/tex]
The Sample Standard Deviation is given by this formula:
[tex]\S =\frac{\sqrt{(x_{i}-\mu)^{2}}}{N-1}\: \s=[/tex]
The Z test shows us the validity of the results.
2)
For the Z test we need the Variance [tex]\sigma ^{2}[/tex]
Z = (M - μ) / √(σ2 / n)
[tex]Z_{score}=\frac{2.3-2.7}{\sqrt{\frac{0.16}{0.15}}}\\Z_{score}= -3.87298[/tex]
3)
Z Test = -3.87298 standard deviation units, since it's a negative value is 3.897 below the mean.
p= .0001 the p value.
Then the results are significant at p values < 0.1
