Consider the following scenarios.I. A group of musicians count how many times they cansnap their fingers in 10 seconds with their dominanthands and with their nondominant hands. They willtest to see if musicians can snap faster with dominanthands than nondominant hands.II. A group of musicians is trying to measure theeffectiveness of practice time. Half of them practicea difficult piece of music for one hour each day whilethe other half practice two hours each day. After aweek, each musician plays the piece as a judge countsthe number of errors. They will test to see if morepractice results in fewer errors.Which are the proper choices for the hypothesis tests?A) Both scenarios require a 2-sample t-test.B) Both scenarios require a matched pairs t-test.C) Scenario I calls for a 2-sample t-test, and Scenario IIcalls for a matched pairs t-test.D) Scenario I calls for a matched pairs t-test, andScenario II calls for a 2-sample t-test.E) The proper tests cannot be determined until we seethe actual data that are collected.
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.
Consider the following scenarios.
I. A group of musicians count how many times they can
snap their fingers in 10 seconds with their dominant
hands and with their nondominant hands. They will
test to see if musicians can snap faster with dominant
hands than nondominant hands.
II. A group of musicians is trying to measure the
effectiveness of practice time. Half of them practice
a difficult piece of music for one hour each day while
the other half practice two hours each day. After a
week, each musician plays the piece as a judge counts
the number of errors. They will test to see if more
practice results in fewer errors.
Which are the proper choices for the hypothesis tests?
A) Both scenarios require a 2-sample t-test.
B) Both scenarios require a matched pairs t-test.
C) Scenario I calls for a 2-sample t-test, and Scenario II
calls for a matched pairs t-test.
D) Scenario I calls for a matched pairs t-test, and
Scenario II calls for a 2-sample t-test.
E) The proper tests cannot be determined until we see
the actual data that are collected.
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