A sample of 105 healthy humans showed an average body temper

A sample of 105 healthy humans showed an average body temperature of 98.1^a F and a sample standard devotion of 0.57degreeF. what is the best point of the body temperature of all healthy humans? A sample of 105 healthy humans showed an average body temperature of 98.1degreeF and a sample standard deviation of 0357degree F, what is the 95% confidence interval of the population mean? A sample of 105 healthy humans showed an average body temperature of 98.1degreeF and a sample standard devotion of 0.67degreeF referring to the confidence intent you for question #16, does the interval contain 98.6degreeF?

Solution

Given that

n = number of healthy humans = 105

Averag body temperature (Xbar) = 98.1 ⁰F

sample standard deviation = 0.57⁰F

The point estimate of the mean body temperature of all healthy womans is µ = 98.1⁰F

The 95% confidence interval for population mean is,

Xbar - E < µ < Xbar + E

Here we use t-distribution because population standard deviation is unknown.

E is the margin of error.

E = tc * s /sqrt(n)

s is sample standard deviation.

c is the confidence level = 0.95

alpha = 1 - c = 1 - 0.95 = 0.05

tc we can find by using EXCEL.

syntax:

=tinv(probability,d.f)

where probability = alpha

d.f. = n - 1 = 105 - 1 = 104

tc = 1.9830

5E = (1.9830 * 0.57) / sqrt(105) = 0.1103

lower limit = Xbar - E = 98.1 - 0.1103 = 97.99

upper limit = Xbar + E = 98.1 + 0.1103 = 98.21

95% confidence interval for population mean is (97.99, 98.21)

Yes 98.1 lies between 97.99 and 98.21.