The Baldwin Piano Company has long argued that their method of teaching people to play the piano is superior to that of its competitors. To estimate any difference in the length of time required to learn the basic techniques, as the new staff analyst for Baldwin, you select 100 students who used your method and find the mean time was 159 hours with s = 38.6 hours for your method. In a sample of 120 students using competitor’s method, the mean was 184 hours with s = 58.6. a) Construct a 99% confidence interval for the difference in means. b) Test the hypothesis, at the 5% level, that the Baldwin method reduces the time needed to learn the piano
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.
The Baldwin Piano Company has long argued that their method of teaching people to play the piano is superior to that of its competitors. To estimate any difference in the length of time required to learn the basic techniques, as the new staff analyst for Baldwin, you select 100 students who used your method and find the
a) Construct a 99% confidence interval for the difference in means.
b) Test the hypothesis, at the 5% level, that the Baldwin method reduces the time needed to learn the piano.
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