# Find the mean and standard deviation of the sampling distribution, Statistics Assignment Homework Help

*label*Mathematics

*timer*Asked: May 26th, 2016

*account_balance_wallet*$10

### Question Description

**1.
**A farmer divided a field into 1-foot by
1-foot sections and tested soil samples from 32 randomly selected sections in
the field. He finds that the mean pH level of the samples is 5.7 with a
standard deviation of 0.26.

**(a) **Find
the mean and standard deviation of the sampling distribution of all possible
soil samples of size . Round to three decimal places.

**(b) **Construct
a 95% confidence interval for the mean pH level of soil samples from every
1-foot by 1-foot section. Show your work. Even if you use technology, show the
expression that is used to determine the margin of error for the interval.
Interpret the interval in a complete sentence.

**(c) **The
farmer tested soil samples from 34 randomly selected sections from another
field. He found the mean pH level of those samples to be 6.1 with a standard
deviation of 0.34. Construct a 95% confidence interval for the difference
between the mean pH levels of all possible soil samples from both fields. Show
your work. Even if you use technology, show the expression that is used to
determine the margin of error for the interval. Interpret the interval in a
complete sentence.

Answer: ?

## Tutor Answer

a) The mean is 5.7. The standard deviation of the sample is 2.6. The standard deviation of all field populations, however, is 2.6 divided by the square root of the number of samples. So for this case, the stardard deviation of all fields (also known as the standard error) is:= 2.6 / sqrt(32)= 2.6 / 5.657= 0.460b) Here is the equation for the confidence interval:= x +/- t * SE...where ...

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