Ten engineers working for start-up companies were asked how long they worked, in hours, per week. the data (in hours) are 70, 45, 55, 60, 65, 55, 55, 60, 50, 55. construct a 90% confidence interval for the population average length of time, in hours, for all engineers at start- ups work per week. (in 2 decimal)

to  

Step-by-step explanation:

Data : 70, 45, 55, 60, 65, 55, 55, 60, 50, 55.

Sample mean =

Sample mean =

Sample mean =

Sample standard deviation  =

Sample standard deviation  =

Sample standard deviation  =

Since n < 30 and population standard deviation is unknown

So we will use t dist.

Confidence interval = 90%

So, significance level =α= 0.1

Degree of freedom = n-1 = 10-1 =9

Now refer the t dist table for t critical

So,

Formula of confidence interval =

Substitute the values

Confidence interval =

Confidence interval = to  

Confidence interval = to  

Hence  a 90% confidence interval for the population average length of time, in hours, for all engineers at start- ups work per week is to  

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq