There are 4 boys and 2 girls from the 7th grade and 3 boys and 5 girls from the 8th grade on the soccer team. The coach will pic
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Part a)
The simple random sample of size n=36 is obtained from a population with
and
The sampling distribution of the sample means has a mean that is equal to mean of the population the sample has been drawn from.
Therefore the sampling distribution has a mean of
The standard error of the means becomes the standard deviation of the sampling distribution.
Part b) We want to find
We need to convert to z-score.
Part c)
We want to find
We convert to z-score and use the normal distribution table to find the corresponding area.
Part d)
We want to find :
We convert to z-scores and again use the standard normal distribution table.
Answer with explanation:
To test the Significance of the population which is Normally Distributed we will use the following Formula Called Z test
→p(Probability) Value when ,z=3.756 is equal to= 0.99992=0.9999
⇒Significance Level (α)=0.01
We will do Hypothesis testing to check whether population mean is different from 25 at the alpha equals 0.01 level of significance.
→0.9999 > 0.01
→p value > α
With a z value of 3.75, it is only 3.75% chance that ,mean will be different from 25.
So,we conclude that results are not significant.So,at 0.01 level of significance population mean will not be different from 25.