Togetherness Are good grades in high school associ-ated with family togetherness? A simple random sample of 142 high-school students was asked how many mealsper week their families ate together. Their responses produced a mean of 3.78 meals per week, with a stand-ard deviation of 2.2. Researchers then matched these responses against the students’ grade point averages. Thescatterplot appeared to be reasonably linear, so they went ahead with the regression analysis, seen below. No appar-ent pattern emerged in the residuals plot. Dependent variable: GPAR-squared = 11.0%s = 0.6682 with 142 - 2 = 140 dfVariable Coefficient SE(Coeff)Intercept 2.7288 0.1148Meals/wk 0.1093 0.0263 a) Is there evidence of an association? Test an appropri-ate hypothesis and state your conclusion. b) Do you think this association would be useful inpredicting a student’s grade point average? Explain.c) Are your answers to parts a and b contradictory?Explain.
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.
Togetherness Are good grades in high school associ-
ated with family togetherness? A simple random sample
per week their families ate together. Their responses
ard deviation of 2.2. Researchers then matched these
scatterplot appeared to be reasonably linear, so they went
ent pattern emerged in the residuals plot.
R-squared = 11.0%
s = 0.6682 with 142 - 2 = 140 df
Variable Coefficient SE(Coeff)
Intercept 2.7288 0.1148
Meals/wk 0.1093 0.0263
ate hypothesis and state your conclusion.
predicting a student’s grade point average? Explain.
c) Are your answers to parts a and b contradictory?
Explain.
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