4. A researcher wanted to examine the effect of a new math study skills program on second graders. Fifteen students took the new study skills program for six weeks and then took a standardized math exam, which is known to have a population mean score of u 80. The scores on the exam for the 15 students (who took the study skills program) are reported below. Scores on the standardized math exam for the 15 students: 79, 85, 86, 75, 82, 84, 85, 81, 75, 84, 78, 90, 85, 83, 80 Test to see whether the students who took the new study skills program have significantly higher test scores than the national average. Perform the appropriate test in SPSS using a .05 a. State the null and alternative hypotheses below b. What type of test should be run on the data (be specific with the exact name of the test)? For example, don't just state " test," but the specific t test used. c. What is the conclusion of the hypothesis test? State the p-value and the decision about the hypothesis test below. (Don't write the results here -that will be done in (d) below -just state p and whether Ho is rejected.) d. What is the effect size for the study? Calculate and report the effect size below. Indicate the magnitude of the effect size according to Cohen's standards and interpret what the effect size means in terms of standard deviation units
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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