Exam 7: Introduction to Sampling Distributions

Which of the following statements is true with respect to the sampling distribution of a proportion?

In a campaign speech,a candidate for governor stated that about 63 percent of the people in the state were in favor of spending additional money on higher education.After the speech,a polling agency surveyed a random sample of 400 people and found 234 people who favored more spending on higher education.Based on the candidate's statement,the probability of finding 234 or fewer is approximately 0.97.

A sampling distribution for a sample of n = 4 is normally distributed with a standard deviation equal to 5.Based on this information,the population standard deviation,σ ,is equal to 10 mph.

Which of the following statements is not consistent with the Central Limit Theorem?

Recently the State Fish and Game planted several thousand tagged fish in a local river.The mean length of these fish,which constitute a population,is 12.6 inches.Yesterday,fishermen caught 100 of these tagged fish.You could expect that the mean length for these fish would be 12.6 inches as well since they come from the population.

The size of the standard error of the sample proportion is dependent on the value of the population proportion and the closer the population proportion is to .50,the larger the standard error for a given sample size will be.

The makers of a particular type of candy have stated that 75 percent of their sacks of candy will contain 6 ounces or more of candy.A consumer group that studies such claims recently selected a random sample of 100 sacks of this candy.Of these,70 sacks actually contained 6 ounces or more.The probability that 70 or fewer sacks would contain 6 ounces or less is approximately 0.1251.

A smaller sample might provide less sampling error than a larger sample from a given population.

If a sample is selected using random sampling methods,the primary reason that the sample mean might be different than the corresponding population mean is that the sample might be biased.

A sampling distribution is the distribution of the individual values that are included in a sample from a population.

A major textbook publisher has a contract with a printing company.Part of the contract stipulates that no more than 5 percent of the pages should have any type of printing error.As a quality control measure,the publisher periodically selects a random sample of n = 100 pages.Then,depending on the proportion of pages with errors,they either say nothing to the printer or they complain that the quality has slipped.Suppose the publisher wants no more than a .10 chance of mistakenly blaming the printer for poor quality,what should the cut-off proportion be?

The State Department of Weights and Measures is responsible for making sure that commercial weighing and measuring devices,such as scales,are accurate so customers and businesses are not cheated.Periodically,employees of the department go to businesses and test their scales.For example,a dairy bottles milk in 1-gallon containers.Suppose that if the filling process is working correctly,the mean volume of all gallon containers is 1.00 gallon with a standard deviation equal to 0.10 gallons.The department's test process requires that they select a random sample of n = 9 containers.If the sample mean is less than 0.97 gallons,the department will fine the dairy.Based on this information,suppose that the dairy wants no more than a 0.05 chance of being fined,which of the following options exist if they can't alter the filling standard deviation?

A major automobile manufacturer has developed a new model car that it claims will average 25 mpg on the highway.A random sample of fifty of these cars was tested and they averaged 24 mpg.This means that the claim made by the auto company is incorrect.

The actual mean fill volume for all bottles of a soft drink product that were filled on a Tuesday is 11.998 ounces.A sample of 64 bottles was randomly selected and the sample mean fill volume was 12.004 ounces.Based upon this information,the sampling error is .006 ounces.

The population mean of income for adults in a particular community is known to be $28,600.Given this information,the sampling distribution of values will be less than this depending on the size of the sample used in developing the sampling distribution.

A population,with an unknown distribution,has a mean of 80 and a standard deviation of 7.For a sample of 49,the probability that the sample mean will be larger than 82 is

If you are sampling from a very large population,a doubling of the sample size will reduce the standard error of the sampling distribution by one-fourth.

A sampling distribution for a sample mean shows the distribution of the possible values for the sample mean for a given sample size from a population.

Explain the impact of the size of the sample on the shape of the sampling distribution.

Suppose it is known that the ages of all employees working for a very large computer company is normally distributed with a mean of 44.2 and a standard deviation of 5.6 years.Given this information,discuss what the sampling distribution for looks like?