Exam 7: Sampling Distributions

The owner of a fish market has an assistant who has determined that the weights of catfish are Normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound.If a sample of 64 fish yields a mean of 3.4 pounds, what is probability of obtaining a sample mean this large or Larger?

True or False: The amount of bleach a machine pours into bottles has a mean of 36 oz.with a standard deviation of 0.15 oz.Suppose we take a random sample of 36 bottles filled by this machine.The sampling distribution of the sample mean has a mean of 36 oz.

True or False: If the population distribution is symmetric, the sampling distribution of the mean can be approximated by the normal distribution if the samples contain 15 observations.

For sample sizes greater than 30, the sampling distribution of the mean will be approximately Normally distributed

The Central Limit Theorem is important in statistics because

True or False: If the population distribution is unknown, in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 30 observations.

True or False: As the sample size increases, the effect of an extreme value on the sample mean becomes smaller.

True or False: If the amount of gasoline purchased per car at a large service station has a population mean of 15 gallons and a population standard deviation of 4 gallons, then 99.73% of all cars will purchase between 3 and 27 gallons.

True or False: The standard error of the mean is also known as the standard deviation of the sampling distribution of the sample mean.

The owner of a fish market has an assistant who has determined that the weights of catfish are Normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound.If a sample of 25 fish yields a mean of 3.6 pounds, what is the Z-score for this observation?

A sample that does not provide a good representation of the population from which it was collected is referred to as a(n)sample.

Which of the following statements about the sampling distribution of the sample mean is Incorrect?

True or False: The Central Limit Theorem ensures that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases.

True or False: For distributions such as the normal distribution, the arithmetic mean is considered more stable from sample to sample than other measures of central tendency.

For sample size 1, the sampling distribution of the mean will be normally distributed

True or False: A sampling distribution is defined as the probability distribution of possible sample sizes that can be observed from a given population.

True or False: The amount of bleach a machine pours into bottles has a mean of 36 oz.with a standard deviation of 0.15 oz.Suppose we take a random sample of 36 bottles filled by this machine.The sampling distribution of the sample mean will be approximately normal only if the population sampled is normal.