Exam 7: Sampling and Sampling Distributions

A PGA (Professional Golf Association)tournament organizer is attempting to determine whether hole (pin)placement has a significant impact on the average number of strokes for the 13^th hole on a given golf course.Historically,the pin has been placed in the front right corner of the green,and the historical mean number of strokes for the hole has been 4.25,with a standard deviation of 1.6 strokes.On a particular day during the most recent golf tournament,the organizer placed the hole (pin)in the back left corner of the green.64 golfers played the hole with the new placement on that day.Determine the probability of the sample average number of strokes exceeding 4.75.

The Central Limit Theorem states that as the sample size increases,the distribution of the sample ____________ approaches the normal distribution.

In the upcoming election for governor,the most recent poll,based on 900 respondents,predicts that the incumbent will be reelected with 55 percent of the votes.What is

The population of all _________________ proportions is described by the sampling distribution of .

If a population is known to be normally distributed,then it follows that the sample mean must equal the population mean.

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 36 download times are selected,calculate the standard deviation of the sampling distribution of the sample mean.

Whenever the population has a normal distribution,the sampling distribution of is normal or near normal distribution:

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5.What is μ_x?

We can randomly select a sample from an infinite population of potential process measurements by sampling the process at different and equally spaced time points.

The College Student Journal (December 1992)investigated differences in traditional and nontraditional students,where nontraditional students are defined as 25 years old or older and working.Based on the study results,we can assume the population mean and standard deviation for the GPA of nontraditional students is µ = 3.5 and σ = 0.5.Suppose a random sample of 100 nontraditional students is selected and the GPA for each student is calculated.What is the probability that the random sample of 100 nontraditional students has a mean GPA greater than 3.42?

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5.Find P( < 48).

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

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches.What is the probability that a randomly selected sample of 4 sheets will have an average length of less than 29.9 inches long?

The College Student Journal (December 1992)investigated differences in traditional and nontraditional students,where nontraditional students are defined as 25 years old or older and working.Based on the study results,we can assume the population mean and standard deviation for the GPA of nontraditional students is µ = 3.5 and σ = 0.5.Suppose a random sample of 100 nontraditional students is selected and the GPA for each student is calculated.Find the interval that contains 95.44 percent of the sample means for nontraditional students.

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

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

According to a hospital administrator,historical records over the past 10 years have shown that 20 percent of the major surgery patients are dissatisfied with after-surgery care in the hospital.A scientific poll based on 400 hospital patients has just been conducted.What is the probability that at least 70 patients will not be satisfied with the after-surgery care?

A sample statistic is an unbiased point estimate of a population parameter if the mean of the populations of all possible values of the sample statistic equals the population parameter.

The sampling distribution of the sample mean is developed by repeatedly taking samples of size n and computing the sample means and reporting the resulting sample means in the form of a probability distribution.

The notation for the standard deviation of the sampling distribution of the sample mean is __________.