A random sample of 170 people was provided with a forecasting problem. Each sample member was given, in two ways, the task of forecasting the next value of a retail sales variable. The previous 20 values were presented both as numbers and as points on a graph. Subjects were asked to predict the next value. The absolute forecasting errors were measured. The sample then consisted of 170 differences in absolute forecast errors (numerical minus graphical). The sample mean of these differences was –2.91, and the sample standard deviation was 11.33. Find and interpret the p-value of a test of the null hypothesis that the population mean difference is 0 against the alternative that it is negative. (The alternative can be viewed as the hypothesis that, in the aggregate, people make better forecasts when they use graphs of past history compared to using numerical values from past history.)
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 random sample of 170 people was provided with a forecasting problem. Each sample member was given, in two ways, the task of forecasting the next value of a retail sales variable. The previous 20 values were presented both as numbers and as points on a graph. Subjects were asked to predict the next value. The absolute forecasting errors were measured. The sample then consisted of 170 differences in absolute forecast errors (numerical minus graphical). The sample
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