Exam 7: Sampling and Sampling Distributions

It has been reported that the average time to download the home page from a government website was 0.9 seconds.Suppose that the download times were normally distributed with a standard deviation of 0.3 seconds.If random samples of 23 download times are selected,describe the shape of the sampling distribution and how it was determined.

If the sample size n is infinitely large,then s² is an unbiased estimator of σ².

Whenever the population has a normal distribution,the sampling distribution of $\bar { X }$ Is normal or near normal distribution:

If we have a sample size of 100 and the estimate of the population proportion is .10,what is the standard deviation of the sampling distribution of the sample proportion?

In a manufacturing process,a machine produces bolts that have an average length of 3 inches with a variance of .03.If we randomly select three bolts from this process,What is the probability the mean length of the bolt is at least 3.16 inches?

The reason sample variance has a divisor of n - 1 rather than n is that it makes the variance an unbiased estimate of the population variance.

Packages of sugar bags for Sweeter Sugar Inc.have an average weight of 16 ounces and a standard deviation of 0.3 ounces.The weights of the sugar packages are normally distributed.What is the probability that 9 randomly selected packages will have a weight in excess of 16.025 ounces?

Find $\mathrm { P } ( 395.4 < \bar { X } < 404.6 )$ If the population mean = 400,?_x = 20,and n = 100.

A manufacturing company measures the weight of boxes before shipping them to the customers.If the box weights have a population mean and standard deviation of 90 lbs.and 24 lbs.respectively,then based on a sample size of 36 boxes,what is the probability that the average weight of the boxes will be less than 84 lbs.?

In random sampling without replacement,each element in the sample will be different.

If p = .9 and n = 40,then we can conclude that the sampling distribution of $\hat { p }$ is approximately a normal distribution.

If the sampled population is exactly normally distributed,then the sampling distribution of $\bar { X }$ is also expected to be normal,regardless of the sample size.

Consider two population distributions labeled A and B.Distribution A is highly skewed and nonnormal,while distribution B is slightly skewed and near normal.In order for the sampling distributions of A and B to achieve the same degree of normality:

There is no easy way to calculate an unbiased point estimate of σ.

If we have a sample size of 100 and the estimate of the population proportion is .10,what is the mean of the sampling distribution of the sample proportion?

The ______________ of a sample statistic is the probability distribution of the population of all possible values of the sample statistic.

In the upcoming governor's election,the most recent poll,based on 900 respondents,predicts that the incumbent will be reelected with 55 percent of the votes.What is $\sigma _ { \bar { X } }$ ?

If a population distribution is known to be normal,then it follows that:

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5.Find $\mathrm { P } ( \bar { X } > 49 )$

Suppose that 60 percent of the voters in a particular region support a candidate.Find the probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 4 percentage points of the actual proportion.