z = (x-mu)/sigma where x is the individual score, mu is the average score and sigma is the standard deviation. Normal distribution gives the z score, while x is the score for an individual. If both x and mu are missing, you would have two unknowns, which require two equations to solve.Inverse Normal can be used to find a z-score, given sufficient information.If X is a random variable with a distribution of N(μ, σ), find:p(µ−3σ ≤ X ≤ µ+3σ)
Approximately 99.74%of the X values are less than three standard deviations from the mean.
The usual statement for a standard score is and you can solve for any one of the four given the other three withIf you also have a probability such asand a normal distribution then you can use the standard normal cumulative distribution function and its inverse to saySo, knowingporzimplies you know the other.You can then extend this for example toor similar results.In many problems, not knowing two ofxorμorσor both ofzandpcould cause difficulties in being able to determine them.Probability percentages may be easier to handle rewritten as decimal fractions:for example,95%=0.9595%=0.95.
In step 1, we need to set up our statistical hypothesis. We will now use the statistical notation of H‐zero or H‐naught to represent the null hypothesis and H‐a to represent the alternative hypothesis.The null hypothesis suggests nothing special is going on; in other words, there is no change fromthe status quo, no difference from the traditional state of affairs, or no relationship – depending on the situation at hand. In contrast, the alternative hypothesis disagrees with this, stating that something is going on, or there is a change from the status quo, or there is a difference from the traditional state of affairs. The alternative hypothesis, Ha, usually represents what we want to check or what we suspect is really going on.In Step 2: We Collect data, check conditions, and Summarize Data We look at sampled data in order to draw conclusions about the entire population. In the case of hypothesis testing, based on the data, you draw conclusions about whether or not there is enough evidence to reject Ho. There is, however, one detail that we would like to add here. In this step we collect data and summarize it. In Step 3 We Assess the Evidence This is the step where we calculate how likely is it to get data like that observed (or more extreme) ASSUMING Ho is true.