Confident Interval
STA3003 Fall 2012
Assignment 5 (Total Points Possible: 15)
Name:
Banner ID:
Instructions: Use this page as your cover page, and attach your groupwork behind your work. Your assignment answers should be in complete and grammatically correct sentences.
1. According to the National Center for Health Statistics (2004), 22.4% of adults are smokers. A random sample of 300 adults is obtained. (a) Describe the sampling distribution of phat, the sample proportion of adults who smoke.
(b) In a random sample of 300 adults, what is the probability that at least 50 are smokers?
(c) Would it be unusual if a random sample of 300 adults results in 18% or less being smokers?
Explain your answer.
2. A machine at K&A Tube & Manufacturing Company produces a certain copper tubing component in a refrigeration unit. The tubing components produced by the manufacturer have a mean diameter of 0.75 inch with a standard deviation of 0.004 inch. The quality-control inspector takes a random sample of 30 components once each week and calculates the mean diameter of these components. If the mean is either less than 0.748 inch or greater than 0.752 inch, the inspector concludes that the machine needs an adjustment. (a) Describe the sampling distribution of the sample mean diameter for a random sample of 30 such components.
(b) What is the probability that, based on a random sample of 30 such components, the inspector will conclude that the machine needs an adjustment when, in fact, the machine is correctly calibrated? 3. In a random sample of 678 adult males 20 to 34 years of age, it was determined that 58 of them have hypertension (high blood pressure). Source: The Centers for Disease Control. (a) Obtain a point estimate for the proportion of adult males 20 to 34 years of age who
Assignment 5 (Total Points Possible: 15)
Name:
Banner ID:
Instructions: Use this page as your cover page, and attach your groupwork behind your work. Your assignment answers should be in complete and grammatically correct sentences.
1. According to the National Center for Health Statistics (2004), 22.4% of adults are smokers. A random sample of 300 adults is obtained. (a) Describe the sampling distribution of phat, the sample proportion of adults who smoke.
(b) In a random sample of 300 adults, what is the probability that at least 50 are smokers?
(c) Would it be unusual if a random sample of 300 adults results in 18% or less being smokers?
Explain your answer.
2. A machine at K&A Tube & Manufacturing Company produces a certain copper tubing component in a refrigeration unit. The tubing components produced by the manufacturer have a mean diameter of 0.75 inch with a standard deviation of 0.004 inch. The quality-control inspector takes a random sample of 30 components once each week and calculates the mean diameter of these components. If the mean is either less than 0.748 inch or greater than 0.752 inch, the inspector concludes that the machine needs an adjustment. (a) Describe the sampling distribution of the sample mean diameter for a random sample of 30 such components.
(b) What is the probability that, based on a random sample of 30 such components, the inspector will conclude that the machine needs an adjustment when, in fact, the machine is correctly calibrated? 3. In a random sample of 678 adult males 20 to 34 years of age, it was determined that 58 of them have hypertension (high blood pressure). Source: The Centers for Disease Control. (a) Obtain a point estimate for the proportion of adult males 20 to 34 years of age who