An economist wants to test if there is any difference in income between Escambia county and Miami-Dade county in Florida. To do this, she collects random samples of residents from both these counties. The information collected from these samples is tabulated below. Assume that both the populations are normally distributed with equal population variances. Escambia County (Population 1) Miami-Dade County (Population 2)
n 1 = 11 n 2 = 15
x ¯ 1 = 36,700 x ¯ 2 = 34 ,700
s 1 = 7800 s 2 = 7375
Set up the null and alternative hypotheses to test the economist’s claim.
a) H_0 : μ1- μ2 is less than or equal to 0 versus H_a: is μ1- μ2 greater than 0b) H_0 : μ1 <μ2 versus H_a: is μ1 is greater than or equal to μ2c) H_0 : μ1 is not equal to μ2 versus H_a: is μ1 is equal to μ2d) H_0 : μ1- μ2 is greater than or equal to 0 versus H_a: is μ1- μ2 is less than 0e) H_0 : μ1- μ2 = 0 versus H_a: is μ1- μ2 not equal t0 0

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?