A researcher is interested in whether doing practice problems helps students to increase their grade on their statistics test. He gets a sample of n =16 students in a statistics class and gives them a test before they do any practice problems. The average score on Test 1 is M1 = 74.83. He then makes them do practice problems and gives the same sample of students another test. The average score on Test 2 is M2 = 82.67. The SS of the difference is 400. What are the null and alternative hypotheses in statistical notation Do you use a one- or two-tailed test? What is the critical/cut-off t value with an alpha level of α = .01? What is the variance? What is the estimated standard error? What is the value of the t statistic? Do we reject or fail to reject the null hypothesis (α = .05)? Why?
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 researcher is interested in whether doing practice problems helps students to increase their grade on their statistics test. He gets a sample of n =16 students in a statistics class and gives them a test before they do any practice problems. The average score on Test 1 is M1 = 74.83. He then makes them do practice problems and gives the same sample of students another test. The average score on Test 2 is M2 = 82.67. The SS of the difference is 400.
What are the null and alternative hypotheses in statistical notation
Do you use a one- or two-tailed test? What is the critical/cut-off t value with an alpha level of α = .01?
What is the variance?
What is the estimated standard error?
What is the value of the t statistic?
Do we reject or fail to reject the null hypothesis (α = .05)? Why?
Calculate and report the effect size values (Cohen’s d & r2). Is it small, medium, or large?
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