Asimple random sample from a population with a normal distribution of 98 body temperatures has x =98.90 °f and s =0.68°f. construct a 90% confidence interval estimate of the standard deviation of body temperature of all healthy humans. is it safe to conclude that the population standard deviation is less than 1.40°f?

°f

is it safe to conclude that the population standard deviation is less than 1.40°f?

a. this conclusion is not safe because 1.40 °f is in the confidence interval.

b. this conclusion is safe because 1.40 °f is in the confidence interval.

c. this conclusion is not safe because 1.40°f is outside the confidence interval.

d. this conclusion is safe because 1.40 °f is outside the confidence interval.

And the best conclusion would be:

D. This conclusion is safe because 1.40 °F is outside the confidence interval.

Step-by-step explanation:

1) Data given and notation  

s=0.68 represent the sample standard deviation  

represent the sample mean  

n=98 the sample size  

Confidence=90% or 0.90  

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .  

2) Calculating the confidence interval  

The confidence interval for the population variance is given by the following formula:  

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:  

Since the Confidence is 0.90 or 90%, the value of and , and we can use excel, a calculator or a table to find the critical values.  

The excel commands would be: "=CHISQ.INV(0.05,97)" "=CHISQ.INV(0.95,97)". so for this case the critical values are:  

And replacing into the formula for the interval we got:  

Now we just take square root on both sides of the interval and we got:  

And the best conclusion would be:

D. This conclusion is safe because 1.40 °F is outside the confidence interval.

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068

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