1A market research firm conducts telephone surveys with a 44

1.A market research firm conducts telephone surveys with a 44% historical response rate. What is the probability that in a new sample of 400 telephone numbers, at least 150 individuals will cooperate and respond to the questions? In other words, what is the probability that the sample proportion will be at least 150/400 = .375?

a.Calculate the probability to 4 decimals.

2.Suppose a random sample of size 40 is selected from a population with = 9. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).

a.The population size is N = 500 (to 2 decimals).

3.The Democrat and Chronicle reported that 25% of the flights arriving at the San Diego airport during the first five months of 2001 were late (Democrat and Chronicle, July 23, 2001). Assume the population proportion is p = .25.

a.What is the probability that the sample proportion will be within +/- .03 of the population proportion if a sample of size 800 is selected (to 4 decimals)?
b.What is the probability that the sample proportion will be within +/- .03 of the population proportion if a sample of size 400 is selected (to 4 decimals)?

Many drugs used to treat cancer are expensive. BusinessWeek reported on the cost per treatment of Herceptin, a drug used to treat breast cancer (BusinessWeek, January 30, 2006). Typical treatment costs (in dollars) for Herceptin are provided by a simple random sample of 10 patients.

Develop a point estimate of the mean cost per treatment with Herceptin.

Develop a point estimate of the standard deviation of the cost per treatment with Herceptin (to 1 decimal).

Solution

Q1.

Normal Distribution
Proportion ( P ) =0.44
Standard Deviation ( sd )= Sqrt (P*Q /n) = Sqrt(0.44*0.56/400)
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X >= 0.375) = (0.375-0.44)/0.0248
= -0.065/0.0248 = -2.621
= P ( Z >-2.621) From Standard Normal Table
= 0.9956