Question

Six human skulls from around 4000 b.c. were measured, and the lengths have a mean of 94.2 mm and a standard deviation of 4.9

Answer 1

Answer:

Step-by-step explanation:

Hello!

You have to estimate the mean length of 4000 b.c. human skulls trough a 95% confidence interval.

You know that

n= 6 human skulls

$\frac{}{X}$= 94.2mm

S= 4.9

Assuming that the variable X: length of a 4000b.c. human skull (mm) has a normal distribution, to construct the interval you have to use the t statistic:

[$\frac{}{X}$ ± $t_{n_1;1-\alpha /2} * \frac{S}{\sqrt{n} }$]

$t_{n-1;1-\alpha /2}= t_{5; 0.975}= 2.571$

[94.2 ± 2.571 * $\frac{4.9}{\sqrt{6} }$]

[89.06; 99.34]mm

With a 95% confidence level you'd expect the interval [89.06; 99.34]mm to contain the value for the average skull length for humans 4000 b.c.

I hope this helps!