Question

In: Statistics and Probability

The following data show the body temperatures (in degrees Fahrenheit) from a random sample of 12...

The following data show the body temperatures (in degrees Fahrenheit) from a random sample of 12 independent healthy people in the United States.

98.5 98.2 99.1 96.6 98.1 98.7 97.5 99.0 97.4 98.3 97.8 98.2

  1. What would be the estimate of the average body temperature of healthy people in the United States.

  2. Find a 95% confidence interval for the average body temperature of healthy people in the United States.

  3. Explain carefully the interval you found in part (b) means.

  4. can you please show proof while figuring out the problems

Solutions

Expert Solution

x (x-xbar)^2
98.5 0.146944
98.2 0.966944
99.1 2.300278
96.6 0.000278
98.1 0.340278
98.7 0.380278
97.5 0.780278
99 0.513611
97.4 0.033611
98.3 0.100278
97.8 0.006944
98.2 1164853
sum 1177.4 1164858
Mean(x)=xbar=sum(x)/n 98.11667
standard deviation(s)=sum(x-xbar)^2/n-1 0.712018
n 12
for 95 % confidence level with degree of freedom (n-1)=11
=1-c%=1-0.05 0.05
degrres of freedom 11
t=critical value obtain using t-table with corresponding df=n-1= 2.200985
Margin of error =t*s/sqrt(n) 0.452395
LCL=xbar-ME 97.66427
UCL=xbar+ME 98.56906

estimate of the average body temperature of healthy people in the United States.is xbar=98.12

#95% confidence interval for the average body temperature of healthy people in the United States. is

(xbar-ME,xbar+ME)

(97.67,98.57)----95 % CI

#One can be 95% confident that the mean body temperature of healthy people in US is between 97.67 and 98.57


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