Directions: for Each Question, Do Each of the Following

Sampling Distributions Name

·  Directions: For each question, do each of the following

Sampling Distributions Name

a.)  Identify the Population of Interest (POI)

b.)  Identify the Variable of Interest (VOI)

c.)  K (what do you know?)

d.)  W (what do you want to know?)

e.)  State and check assumptions (conditions) for the sampling distribution.

f.)  Draw a picture and label the parameters for the sampling distribution.

g.)  Calculate the probability

h.)  L (what did you learn?) Write a statement in context of the situation.

1.  A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let denote the proportion in the sample that say they support the increase. Suppose that 40% of all adults in Ohio support the increase. What is the probability that the proportion in the sample () is greater than 42%?

2.  The incomes in a certain large population of college teachers have a normal distribution with mean $35,000 and standard deviation $5,000. Four teachers are selected at random from this population to serve on a salary review committee. What is the probability that their average salary () exceeds $40,000?

3.  Suppose that 20% of the subscribers of a cable television company watch the shopping channel at least once a week. The cable company is trying to decide whether to replace this channel with a new local station. A survey of 100 subscribers will be undertaken. The cable company has decided to keep the shopping channel if the sample proportion () is greater than .25. What is the approximate probability that the cable company will keep the shopping channel, even though the true proportion who watch it is only 20%?

4.  Although a lecture period at a certain university lasts exactly 50 minutes, the actual lecture time of a statistics instructor on any particular day has a distribution with mean value 52 min. and standard deviation 3 min. Suppose that times of different lectures are independent of one another. Let represent the mean of 36 randomly selected lecture times. What is the probability that the mean leacture time of this sample will be less than 50 minutes?

5.  The amount of money spent by a customer at a discount store has a mean of $100 and a standard deviation of $30. What is the probability that a randomly selected group of 50 shoppers will spend a total of more than $5300? (Hint: The total will be more than $5300 when the sample average exceeds what value?)