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

X is the mean annual income of the sample ($50,350)M is the mean annual income assumed under null hypothesis ($50,000)s is the population standard deviation ($2,000)N is the sample size (100)

Then z= =

1.75.

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

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12