Suppose that a researcher is interested in the possible relationship between the amount of screen time each day (X) and the IQ of school-age children (Y). She reasons that increased screen time might be related to lower IQ scores. Suppose that data on these variables were collected from 45 children, with the following outcomes: The sum of squares for daily hours of screen time is 53, the sum of squares for the IQ scores is 4980, and the sum of the products of the deviation scores is -250. Based on this information, calculate the appropriate test (by hand) at the 5% level of significance. Decide on a 1-tail or 2-tail test based on the goals of the research. Provide your answers in the spaces provided; do NOT show your work in the blanks. The value for the calculated test statistic = . You must only write your final calculated answer for the test statistic. The critical value =
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.
Suppose that a researcher is interested in the possible relationship between the amount of screen time each day (X) and the IQ of school-age children (Y). She reasons that increased screen time might be related to lower IQ scores. Suppose that data on these variables were collected from 45 children, with the following outcomes: The sum of squares for daily hours of screen time is 53, the sum of squares for the IQ scores is 4980, and the sum of the products of the deviation scores is -250.
Based on this information, calculate the appropriate test (by hand) at the 5% level of significance. Decide on a 1-tail or 2-tail test based on the goals of the research. Provide your answers in the spaces provided; do NOT show your work in the blanks.
The value for the calculated test statistic = . You must only write your final calculated answer for the test statistic.
The critical value =
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