A possible starting team for the 2013-14 New York Knicks is shown in the following table. Player Position Height (inches) Raymond Felton(R) Guard 73 J.R.Smith(J) Guard 78 Iman Shumpert(I) Forward 77 Carmelo Anthony(C) Forward 80 Andrea Bargnani(A) Center 84 a) Calculate the population mean height, , of the five players. b) For samples of size 2, construct a table similar to the table in Sec 7.1. Use the letter in parentheses after each player’s name to represent each player. c) Draw a dotplot for the sampling distribution of the sample mean for samples of size 2. d) For a random sample of size 2, what is the chance that the sample mean will equal the population mean? e) For a random sample of size 2, obtain the probability that the sampling error made in estimating the population mean by the sample mean will be 1 inch or less; that is, determine the probability that will be within 1 inch of . Interpret your results in terms of percentages.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A possible starting team for the 2013-14 New York Knicks is shown in the following table.
Player Position Height (inches)
Raymond Felton(R) Guard 73
J.R.Smith(J) Guard 78
Iman Shumpert(I) Forward 77
Carmelo Anthony(C) Forward 80
Andrea Bargnani(A) Center 84
- a) Calculate the population mean height, , of the five players.
- b) For samples of size 2, construct a table similar to the table in Sec 7.1. Use the letter in parentheses after each player’s name to represent each player.
- c) Draw a dotplot for the sampling distribution of the sample mean for samples of size 2.
- d) For a random sample of size 2, what is the chance that the sample mean will equal the population mean?
- e) For a random sample of size 2, obtain the probability that the sampling error made in estimating the population mean by the sample mean will be 1 inch or less; that is, determine the probability that will be within 1 inch of . Interpret your results in terms of percentages.
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