Researchers are studying rates of homeowners in a certain town. they believe that the proportion of people ages 36-50 who own homes is signifificantly greater than the proportin of people age 21-35 who own homes and want to test this claim. the results of the surverys are: homeowners renters total
ages 21-35 18 38 56

ages36-50 40 22 62
total 58 60 118

what are the null hypothesis and alternative hypothesis for this situation

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?