Hello Hope someone could help m with my homwork in my stats

Hello, Hope someone could help m with my homwork in my stats class..

Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 40 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that = 7.50 ml/kg for the distribution of blood plasma.

(a) Find a 95% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Use 2 decimal places.) lower limit upper limit moe

(b) What conditions are necessary for your calculations? (Select all that apply.)

is known

is unknown

the distribution of weights is uniform

n is large

the distribution of weights is normal

(c) Give a brief interpretation of your results in the context of this problem.

5% of the intervals created using this method will contain the true average blood plasma volume in male firefighters.

95% of the intervals created using this method will contain the true average blood plasma volume in male firefighters.

The probability that this interval contains the true average blood plasma volume in male firefighters is 0.95.

The probability that this interval contains the true average blood plasma volume in male firefighters is 0.05.

(d) Find the sample size necessary for a 95% confidence level with maximal/marginal error of estimate E = 2.60 for the mean plasma volume in male firefighters.

Solution

a)
Margin of Error = Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
Mean(x)=37.5
Standard deviation( sd )=7.5
Sample Size(n)=40
Margin of Error = Z a/2 * 7.5/ Sqrt ( 40)
= 1.96 * (1.186)
= 2.324

CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=37.5
Standard deviation( sd )=7.5
Sample Size(n)=40
Confidence Interval = [ 37.5 ± Z a/2 ( 7.5/ Sqrt ( 40) ) ]
= [ 37.5 - 1.96 * (1.186) , 37.5 + 1.96 * (1.186) ]
= [ 35.176,39.824 ]

b)
is known

c)
95% of the intervals created using this method will contain the
true average blood plasma volume in male firefighters.

d)
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.05% LOS is = 1.96 ( From Standard Normal Table )
Standard Deviation ( S.D) = 7.5
ME =2.6
n = ( 1.96*7.5/2.6) ^2
= (14.7/2.6 ) ^2
= 31.966 ~ 32