Exam 7: Sampling Distributions

Rh-Positive Blood Type Narrative The proportion of individuals with an Rh-positive blood type is 88%. You have a random sample of n = 500 individuals. -Refer to Rh-Positive Blood Type Narrative. Between which two limits would the sample proportion lie 99% of the time?

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. What is the probability that the average IQ of this sample is below 108?

A newspaper is trying to decide which comics to carry on a daily basis, which comics to carry only on Sunday, and which comics to discontinue. The editor invites the readers to "vote" for their preferences by clipping a "ballot" from the editorial page and mailing it in. This is an example of a judgment sample.

Given a population proportion of p = 0.8 and a sample size of n = 100, what is the standard deviation of the sampling distribution of the sample proportion, ?

Stratified random sampling involves selecting a simple random sample from each of a given number of subpopulations, called strata.

The Central Limit Theorem is used to describe the sampling distributions of statistics, such as and , when the population is known to be normally distributed.

Random cause variation refers to variation in the output of a process that is unexpected and has an assignable cause.

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. -Refer to Baggage Weights Narrative. What are the mean and standard deviation of the sampling distribution of , the sum of the sample measurements?

Fuel Consumption of Cars Narrative Suppose the average fuel consumption (in litres per 100 km) of a particular model car is 8.4 L/100 km with a standard deviation of 2.4 L/100 km. A random sample of 64 cars of this model is selected. -Refer to Fuel Consumption of Cars Narrative. Describe the sampling distribution of .

The sampling distribution of the sample mean is exactly normally distributed, regardless of the sample size n.

MRI Accuracy Narrative A group of medical researchers reported on the accuracy of using magnetic resonance imaging (MRI) to evaluate ligament sprains and tears on 50 patients. Consecutive patients with acute or chronic knee pain were selected from the clinical practice of one of the researchers and agreed to participate in the study. -Refer to MRI Accuracy Narrative. Describe the sampling plan used to select study participants.

The distribution of scores for the 1000 final exams in a statistics course has a mean of 74 and a standard deviation of 15. A random sample of 36 exam papers is selected. What is the probability that the sample mean is higher than 77?

Stress and Sweets Narrative According to one study, 50% of Canadians admit to overeating sweet foods when stressed. Suppose that the 50% figure is correct and that a random sample of n = 100 Canadians is selected. -Refer to Stress and Sweets Narrative. Does the distribution of the sample proportion of Canadians who relieve stress by overeating sweet foods, have an approximately normal distribution? If so, what are its mean and standard deviation?

The population of pop cans filled by a particular machine is known to be normally distributed with a mean of 12 ounces and a standard deviation of 0.16 ounces. Given this information, the sampling distribution of the sample mean, , for a random sample of 16 cans will also be normally distributed with a standard deviation equal to 0.04.

Unemployment Rate Narrative An eastern province has an unemployment rate of 6%. The province conducts monthly surveys in order to track the unemployment rate. In a recent month, a random sample of 700 people showed that 35 were unemployed. -Refer to Unemployment Rate Narrative. If Find the probability that the sample unemployment rate is at most 5%.

Examination Times Narrative The time necessary to complete an examination has a mean of 45 minutes and a standard deviation of 4 minutes. The average time necessary for 64 randomly selected students is computed. -Refer to Examination Times Narrative. Can we say that the sampling distribution of is approximately normally distributed? Why?

What is the term for a numerical descriptive measure calculated from a sample?

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. Will there be an equal number of patients in each treatment group? Explain.

Examination Times Narrative The time necessary to complete an examination has a mean of 45 minutes and a standard deviation of 4 minutes. The average time necessary for 64 randomly selected students is computed. -Refer to Examination Times Narrative. What is the standard deviation of the sampling distribution of ?

A questionnaire was mailed to 1000 registered municipal voters selected at random. Only 500 questionnaires were returned, and of the 600 returned, 450 respondents were strongly opposed to a surcharge proposed to support the city Parks and Recreation department. Are you willing to accept the 75% figure as a valid estimate of the percentage in the city who are opposed to the surcharge? Why or why not?