Solve the following problems about thesampling distribution.

Statistical inference or educated guessing using statisticaltechniques and data analysis may be biased if completed based on one and only one data point.

1. True
2. False

Statistical inference based on one and only one data point may be biased in partbecausethe data point may be unrepresentative of most other data points in the collection.

1. True
2. False

What is the word for such an unrepresentative data point?

ANSWER:

Instead of utilizing a single data point,statisticians use a sample statistic such as the sample mean oras the basis for theirstatistical inference.

1. True
2. False

Thesampling distributionofxis theprobability distributionfor all possible values of the sample mean,x.

True

False

The sampling distribution is the relative frequency of each possible sample mean occurring in a population.

1. True
2. False

Mrs. Montanez, dispatcher at Quicksilver Bus Company, needs to pulltwo of fiveschool buses off their regularly scheduled early morning routes for an emergency inspection, following a series of minor, non-critical mechanical failures.Replacement coaches will be sent, but with a slight delay.She randomly chooses two of the buses for this urgent attention.The buses all operate in the same town and are designated by the neighborhood they serve: Alpine (A), Beachwood (B), Chelsea (C), Downtown (D), and Eastside (E).She also wonders how many students, on average, her decision will inconvenience.

Bus A B C D E

Number of Students 24 30 21 18 27

To assist Mrs. Montanez, select asimple random sampleof buses,n, from the population of size,N.

What is the sample size?Answer:

What is the population size?Answer:

Mrs. Montanez, dispatcher at Quicksilver Bus Company, needs to pulltwo of fiveschool buses off their regularly scheduled early morning routes for an emergency inspection, following a series of minor, non-critical mechanical failures.Replacement coaches will be sent, but with a slight delay.She randomly chooses two of the buses for this urgent attention.The buses all operate in the same town and are designated by the neighborhood they serve: Alpine (A), Beachwood (B), Chelsea (C), Downtown (D), and Eastside (E).She also wonders how many students, on average, her decision will inconvenience.

Bus A B C D E

Number of Students 24 30 21 18 27

To assist Mrs. Montanez, select asimple random sampleof buses,n, from the population of size,N.

If the first sample isAB, what are the others?Write them symbolically and alphabetically using the capitalized first letter of eachlocation:

Answer: Answer: Answer: Answer: Answer:

Answer: Answer: Answer: Answer:

For this example about the buses being selected in pairs from a total of five buses, computeofflineeach possible sample mean, andthencompute the grand mean or mean of all the possible sample means.

Answer:

For this example about the buses, compute the population mean for the original data values.

Answer:

For this example,does the grand mean equal the population mean?

1. Yes
2. No

The expected value or mean of thesampling distributionofxis ux.

True

False

The mean of all the possible sample means(x) that could be taken from a populationis sometimes referred to as the grand mean, orx (x-double-bar, orxwith a double overstrike).

True

False

The grand meanXdoes not equal the mean of the original population.In otherwords,X=U

1. True
2. False

The spread of thesampling distributionofxdecreases as sample size,n,increases and vice-versa, as indicated by the formula:Ox=O/v-n.

True

False

Thestandard deviationof thesampling distributionofxis also referred to as thestandard error of the mean.

True

False

According to theCentral Limit Theorem, in selecting simple random samples of size,n, from a population with mean,u, and standard deviation, , the sampling distribution ofapproaches a normal probability distribution with mean,u, andstandard deviation,o/v-n, as the sample size becomes infinitely large.

True

False