Exam 7: Sampling Distributions

College Football Division Narrative A student government representative at a local university claims that 60% of the undergraduate students favour a move to Division I in college football. A random sample of 250 undergraduate students is selected. -Refer to College Football Division Narrative. Find the probability that the sample proportion exceeds 0.65.

Process control charts, such as the and p charts, are used to provide signals to indicate when the output of a process is out of control.

Given a sampling distribution of the sample mean, , that is normally distributed and has a mean of 30 and a standard deviation of 8, to which of the following does a sample mean of 40 correspond?

The scores of a class are normally distributed with a mean of 82 and a standard deviation of 8. What is the probability that the mean score of a sample of 64 students is at least 80?

Which of the following is a commonly used parameter?

Standard error of the sample proportion is another term for the variance of the sampling distribution of the sample proportion, .

Given a population variance of = 36 and a sample size of n = 9, which of the following would equal the standard deviation of the sampling distribution of the sample mean, ?

The mean of the sampling distribution of sample mean, , is equal to the mean of the population from which the samples are selected to construct the sampling distribution.

The population of incomes in a community college in Ontario is thought to be highly skewed to the right with a mean equal to $38,765 and a standard deviation equal to $2,640. Based on this information, if a sample of size 36 is selected at random, then the highest sample mean that we would expect to see would be approximately $40,085.

Heights of Adult Males Narrative The distribution of heights of adult males has a mean of 175.0 cm and a standard deviation of 10.0 cm. A random sample of 36 adult males is selected. -Refer to Heights of Adult Males Narrative. Completely describe the sampling distribution of .

The mean for a sample selected randomly from a population is most likely to be lower or higher than the known value of the population mean.

Baggage Weights Narrative The weight of baggage checked by airline passengers is a random variable with a mean of 25 kg and a standard deviation of 12 kg. The total baggage limit for 100 randomly selected passengers is 2740 kg. -A population consists of four numbers, 0, 1, 2, and 4. Suppose we randomly select two of those four numbers without replacement and compute the sample mean, , of the two numbers selected. Find the sampling distribution of .

Lifetime of Fluorescent Light Bulbs The mean lifetime of a fluorescent light bulb is 1570 hours with a standard deviation of 200 hours. Suppose we take a sample of 100 bulbs, test them, and calculate the sample mean. -Refer to Lifetime of Fluorescent Light Bulbs. Completely describe the sampling distribution of the sample mean.

Weights of Chocolate Bars Narrative A candy bar factory is pouring chocolate into moulds to cool. The finished bars are sold as 35 gram bars. The company will lose money if the moulds are overfilled. If the moulds are underfilled, the weight of the candy bars will be less than the wrapper label says, and the company will be subject to a fine for misrepresenting the size of its product. The company wants to create an chart to monitor the weight of the candy bars. Suppose 5 samples are taken, each of size 30, having the sample means 36.1, 34.6, 35.8, 34.9, and 35.8 grams, respectively. -Refer to Weights of Chocolate Bars Narrative. How is the chart used in this situation?

The Central Limit Theorem can be applied to the sampling distribution of the sample proportion, , regardless of the sample size, n, and the population proportion, p.

Blood Thinner Study Narrative A study of an experimental blood thinner was conducted to determine whether it works better than the simple aspirin tablet in warding off heart attacks and strokes. The study involved 20,000 people who had suffered heart attacks, strokes, or pain from clogged arteries. Each person was randomly assigned to take either aspirin or the experimental drug for one to three years. Assume that each person was equally likely to be assigned one of the two medications. -Refer to Blood Thinner Study Narrative. Devise a randomization plan to assign the medications to the patients.

IQ of Elementary School Children Narrative In a particular large school system, the average IQ of elementary school children is 105 and the standard deviation is 15. A sample of 81 children is randomly selected from elementary schools within the system. -Refer to IQ of Elementary School Children Narrative. Find the mean and standard deviation of the sampling distribution of .

The distribution of the time that a battery pack for a laptop computer can function before requiring recharging is normal with a mean of 6 hours and a standard deviation of 1.8 hours. A random sample of 25 laptops with this type of battery pack is selected and tested. What is the probability that the mean time until recharging is necessary is at least 7 hours?

If the variation in a process variable is solely random, the process is said to be in control.

Defective Items Narrative Suppose a sample of 120 items is drawn from a population of manufactured products and the number of defective items is recorded. Prior experience has shown that the proportion of defectives is 0.05. -Refer to Defective Items Narrative. Use the results of the previous question to find the probability that is greater than 0.23.