Exam 9: Sampling Distributions

The accuracy of the approximation of with a normal distribution depends on the probability distribution of the ____________________ and on the sample ____________________.

The variance of the sampling distribution of is ____________________ the variance of the population we're sampling from for all sample sizes.

Suppose the ages of students in your program follow a positively skewed distribution with mean of 24 years and a standard deviation of 4 years.If we randomly sampled 100 students,which of the following statements about the sampling distribution of the sample mean age is NOT true?

The amount of bleach a machine pours into bottles has a mean of 50 ounces with a standard deviation of 0.25 ounces.Suppose we take a random sample of 36 bottles filled by this machine.The sampling distribution of the sample mean has a standard error of 0.25 ounces.

A sample of 250 observations is selected at random from an infinite population.Given that the population proportion is .25,the standard error of the sampling distribution of the sample proportion is:

Average Annual Revenue Suppose that the average annual revenue of a small business is $150,000 with a standard deviation of $40,000.Assume that the revenue distribution is normal. ​ ​ -{Average Annual Revenue Narrative} What is the probability that one business selected at random makes less than $120,000?

If two random samples of sizes n₁ and n₂ are selected independently from two populations with variances and ,then the standard error of the sampling distribution of the sample mean difference, ,equals:

The expected value of is ____________________.

If a random sample of size n is drawn from a normal population,then the sampling distribution of the sample mean will be:

The standard deviation of is also called the ____________________ of the sample proportion.

A sample of size n is selected at random from an infinite population.As n increases,the standard error of the sample mean increases.

A randomly selected value of is likely to be ____________________ to(than)the mean of the population than is a randomly selected value of X.

If two populations are normally distributed,the sampling distribution of the difference in the sample means, ,is:

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

If two samples are selected independently from two non-normal populations,then the sampling distribution of is only approximately normal provided that either n₁ or n₂ is 30 or more.

The Central Limit Theorem states that,if a random sample of size n is drawn from a population,then the sampling distribution of the sample mean :

Poker Time The amount of time spent by American adults playing Poker per week is normally distributed with a mean of 4 hours and standard deviation of 1.25 hours. ​ ​ -{Poker Time Narrative} Find the probability that if four American adults are randomly selected,all four play Poker for more than 5 hours per week.

If all possible samples of size n are drawn from an infinite population with standard deviation 8,then the standard error of the sample mean equals 1.0 if the sample size is 64.

The estimator of the probability of success in a binomial distribution is: ____________________.

Number of Fish Tanks The following data give the number of fish tanks owned for a population of 4 families. ​ ​ -{Number of Fish Tanks Narrative} List all possible samples of 2 families that can be selected without replacement from this population,and compute the sample mean for each sample.