Words were displayed on a computer screen with one of two background colors: red or blue. The subjects were then asked to recall the words that were displayed. There were 35 subjects who were shown words on red backgrounds; they scored a mean score of 15.89 words on the memory test, with a standard deviation of 5.90 words. The 36 subjects shown words on a blue background had a mean score of 12.31 words on the memory test, with a standard deviation of 5.48 words. Constructa 95% confidence interval to estimate the difference between the two population means. a) List the degrees of freedom for this experiment. Find the critical number that is relevant to the results using a 95% confidence level. b) Find the margin of error E that corresponds to a 95% confidence level. RoundEto 5 decimal places. c) Find the 95% confidence interval estimate of the difference of the population means, (μ1−μ2). Follow rounding rules and use appropriate notation. d) Based on the confidence interval estimate, is there a significant difference between the two means? Why or why not? If there is, which color appears to be associated with higher scores?
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.
Words were displayed on a computer screen with one of two background colors: red or blue. The subjects were then asked to recall the words that were displayed. There were 35 subjects who were shown words on red backgrounds; they scored a
a) List the degrees of freedom for this experiment. Find the critical number that is relevant to the results using a 95% confidence level.
b) Find the margin of error E that corresponds to a 95% confidence level. RoundEto 5 decimal places.
c) Find the 95% confidence
d) Based on the confidence interval estimate, is there a significant difference between the two means? Why or why not? If there is, which color appears to be associated with higher scores?
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