Exam 6: Sampling Distributions

As the sample size ___________,the variability of the sampling distribution of the sample proportion increases.

The sampling distribution of the sample mean is approximately normal for sufficiently ________ sample sizes regardless of the distribution shape of the sampled population.

If a population is known to be normally distributed,then it follows that the sample mean $\bar { x }$ must equal the population mean $\mu$ .

The diameter of small toy balls manufactured at a factory is expected to be approximately normally distributed with a mean of 5.2 cm and a standard deviation of .08 cm. Suppose a random sample of 20 balls are selected. -Calculate the standard deviation of the sampling distribution of the sample mean.

If the sampled population is finite and at least _____ times larger than the sample size,then the finite population multiplier is approximately equal to one.

The ___________ is a minimum-variance unbiased point estimate of the population mean.

As the sample size increases,the mean of the sampling distribution of $\bar { x }$ decreases.

The sample standard deviation s is an unbiased estimator of the population standard deviation $\sigma$ .

In the upcoming students' council election, the most recent poll based on 900 students predicts that the incumbent will be re-elected with 55% of the votes. -What is $\sigma _ { \hat { p } }$ ?

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 cm and a standard deviation of 0.3 cm.What is the probability that average length of a steel sheet from a sample of 9 units is more than 29.95 cm long?

A random sample of size 1,000 is taken from a population where, for some characteristic of the population, p = .20. -What is $\mu _ { \hat { p } }$ ?

Suppose you take a random sample from a normally distributed population with mean $\mu$ = 2500 and compute the sample mean )If $\sigma _ { \bar { x } } ^ { 2 }$ = 7,find P( $\bar { x }$ > 2510).

Packages of sugar bags for Sweeter Sugar Inc.have an average weight of 16 grams and a standard deviation of 0.2 grams.The weights of the sugar bags are normally distributed.What is the probability that 16 randomly selected packages will have a weight in excess of 16.075 grams?

Suppose you take a random sample of size n = 81 from a population with $\mu$ = 1000 and $\sigma$ = 90.Find P( $\bar { x }$ > 1015).

If p = .8 and n = 50,then we can conclude that the sampling distribution of $\hat { p }$ is approximately a normal distribution.

As the sample size ______________ the variance of the sampling distribution of $\bar { x }$ ___________.

The chief chemist for a major oil/gasoline production company claims that the regular unleaded gasoline produced by the company contains on average 4 grams of a certain ingredient. The chemist further states that the distribution of this ingredient per L of regular unleaded gasoline is normal and has a standard deviation of 1.2 grams -What is the probability of finding an average in excess of 4.3 grams of this ingredient from randomly inspected 100L of regular unleaded gasoline?

What are the mean and the standard deviation of the sampling distribution of $\hat { p }$ ?

A minimum variance unbiased point estimate has a variance that is as small as or smaller than the variances of any other unbiased point estimate.

The mean of the sampling distribution of $\bar { x }$ is always equal to the mean $\mu$ of the sampled population.