Question

(1 point) Archeologists have discovered a sample of ancient Egyptian skulls from 150 A.C. A sample of 10 Egyptian skull breadths (in mm) from 150 A.C. is show below: Skull breadths Sample: 137, 134, 134, 127, 130, 135, 136, 129, 131, 130 Part 1: Calculate the mean and standard deviation for for the data set. Round the mean to 2 decimal places, and the standard deviation to 4 decimal places 150 A.C. skull breadths mean: 132.30 150 A.C. skull breadths standard deviation: 3.3350 Part 2: Using your answers from part 1 and the formula for a 98% confidence interval as presented in lecture, fill in the blanks with the appropriate values for this problem for calculating the confidence interval below. To enter V where x is any number, type sqrt(x). For example, V2 should be written as sqrt(2) 150 A.C. skull breadths: to

Answer 1

the confidence interval for mean is given by

$(\bar{x}-t_\alpha\frac{s}{\sqrt{n}})\ to\ (\bar{x}+t_\alpha\frac{s}{\sqrt{n}})$

we have sample mean ,

$\bar{x}=132.3$

sample standard deviation ,

$s=3.3350$

for 98% confidence interval with n - 1= 9 degrees of freedom , we get t value as

$t_\alpha=2.821$

we can write interval as

$\boldsymbol{132.3-2.821(\frac{3.335}{\sqrt{10}})\ \ to \ \ 132.3+2.821(\frac{3.335}{\sqrt{10}})}$