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#### Finding t critical values for Hypothesis Testing – sigma unknown

First, find the t-critical value for right-tailed tests. There are two steps to find it. However, before starting check to see if the population standard deviation,σ, is given or not. Check the second condition, either the sample size is more than or equal to 30 or the population is normally distributed. Step 1, identify the...

#### Finding t critical values for Confidence Interval – sigma unknown

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#### Finding z critical values for Hypothesis test

In summary, in order to find z-critical values, we need to find the left cumulative area to look up the z-table. For left-tailed tests, since we have the left area as the significance level for the test, we use that α to find the z critical value However, for right-tailed tests, we need to subtract...

#### Finding t critical values for Hypothesis testing

In summary, we need to find the degree of freedom and one-tailed area to look up the t-table.  Please make sure that our t-table gives only positive t-scores. Therefore, we need to switch positive t-scores to negative values for left-tailed tests and must have both positive and negative values for two-tailed tests.

#### Finding z critical values for Confidence Interval

Since we use the left cumulative z-table, we need to find the left-tailed area to find the negative z-critical value. First, subtract the given confidence level from one and then divide it by 2 to get the left area. Look up the table using the left area to find one of the critical values. Once...

#### Finding t critical values for Confidence Interval

we need to find the degree of freedom and one-tailed area to look up the t-table.  Please make sure to state both positive and negative critical values since our t-table only gives positive values.

#### Calculating Standard Deviation by Hand

When you calculate the standard deviation,make sure to use the mean. Once you find the sum of the squared deviations, you already have the numerator value of the formula. To find the number of the observations, you just count the number of x values.

#### The Normal Distribution Finding Area

We looked at three types of examples, finding the left area, right area, and between area. In any case, we have to look up the table to find the left cumulative area that corresponds to z-scores.   Please keep in mind that our z-table always gives the left cumulative area. For finding the left area of...

#### Probability by Tree Method

A probability tree is a simple and effective method of applying the probability rules by representing events in an experiment by lines.  It is shown as two levels and two branches.

#### The Normal Distribution Finding z scores

In summary, we use the left cumulative area to find z-scores.  If the right area is given, then subtract the right area from 1 to look up the table.
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