Question

1. A random sample of 36 skeletal remains from females was taken from data stored in the Forensic Anthropology Data Bank (FDB) at the University of Tennessee. The femur lengths (right leg) in millimeters are recorded below.

432	432	435	460	432	440	448	449	434	443
525	451	448	443	450	467	436	423	475	435
433	438	453	438	435	413	439	442	507	424
468	419	434	483	448	514

a. Determine the sample mean and standard deviation.

b. Since the sample size is large, we can use the sample standard s in place of σ in calculations of confidence intervals.

c. Before doing any calculations, think about a 90%, 95% and 99% confidence for µ, the mean femur bone length for women. Which of these intervals would be the widest? Which would be the narrowest? Explain how you know without calculating the confidence intervals.

d. Calculate 90%, 95%, and 99% confidence intervals for µ, the mean femur bone length for adult females. Do your results confirm your answer to (b)?

e Redo the 95% confidence interval using the 68-95-99.7 Rule. Comment on the difference between this and the answer you got in part d.

f. How much can a single outlier affect a confidence interval? Suppose that the first observation of 432 millimeters had been mistakenly entered as 4.32 millimeters.

(i) Make a boxplot of the modified data set to show that this short femur length is an outlier.

(ii) Recalculate the 95% confidence interval based on the modified data. How much did the outlier affect the confidence interval?

Answer 1

a. The sample mean= = 16146=448.5 mm and

standard deviation= = 25.292mm

b. Yes, Since the sample size is large, we can use the sample standard s can replace place of σ in calculations of confidence intervals.

c. Before doing any calculations, thinking about a 90%, 95% and 99% confidence for µ, the mean femur bone length for women. 99% intervals will be the widest.  90% will be the narrowest.

Without calculating the confidence intervals is the 99%, 95%, 90%confidence interval respectively

d. 90% confidence intervals for µ,=406.89466 mm to 490.10534mm

95%confidence intervals for µ =398.92768 mm to 498.07232mm

99% confidence intervals for µ = 383.24664 mm to 513.75336mm

Yes, theresults confirm my answer to (b).

e the 95% confidence interval using the 68-95-99.7 Rule. 95%confidence intervals for µ =397.916 mm to 513.75336mm, replacing 1.96 by 2.

The difference between this and the answer I got in part d is marginally wider as I replaced 1.96 in (d) by 2.