The mean annual incomes of certified welders are normally distributed with the mean of $50,000 and a population standard deviation of $2,000. the ship building association wishes to find out whether their welders earn more or less than $50,000 annually. a sample of 100 welders is taken and the mean annual income of the sample is $50,350. if the level of significance is 0.10, what conclusion should be drawn?

a. do not reject the null hypothesis as the test statistic is less than the critical value of z.
b. do not reject the null hypothesis as the test statistic is less than the critical value of t.
c. reject the null hypothesis as the test statistic is greater than the critical value of t.
d. reject the null hypothesis as the test statistic is greater than the critical value of z.

D. Reject the null hypothesis as the test statistic is greater than the critical value of z.

Step-by-step explanation:

welders earn $50,000 annually

welders' income does not equal $50,000 annually

Sample size 100>30, therefore we need to calculate z-values of sample mean and significance.

z-critical at 0.10 significance is 1.65

z-score of sample mean (test statistic) can be calculated as follows:

where

Then z= =

1.75.

Since test statistic is bigger than z-critical, (1.75>1.65), we reject the null hypothesis.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.