Hypothesis: a statement (or claim) about a property/characteristic of a population.
Hypothesis testing: a procedure, based on sample evidence and probability, for testing claims about a property/characteristic of a population.
Null Hypothesis (H0): A statement of no change, no effect, or no difference. Assumed true until evidence indicates otherwise. We either reject or fail to reject H0.
Alternative Hypothesis (Ha): A statement that we are trying to find evidence to support; contradictory to H0.
The test statistic: Measures the difference between the sample result and the null value.
p-value: the probability that, if the null hypothesis is true, the results from another randomly selected sample will be as extreme or more extreme as the results obtained from the given sample.
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One-tailed tests: Left- and right-tailed tests. The alternative hypothesis changes; the null hypothesis remains the same in all three tests.
Left-tailed tests: “too small” values of the statistic as compared to the hypothesized parameter value lead to the rejection of the null hypothesis.
Right-tailed tests: “too-large” values of the statistic as compared to the hypothesized parameter a=value lead to the rejection of the null hypothesis.
Step 1→ Determine the null and alternative hypotheses.
Step 2→ Verify all conditions have been met and state the level of significance.
Step 3→ Summarize the data into an appropriate test statistic.
Step 4→ Find the p-value by comparing the test statistic to the possibilities expected if the null hypothesis were true OR determine the critical value.
Step 5→ Decide whether the result is statistically significant based on the p-value.
Step 6→ Report the conclusion in the context of the situation.
Acronym for steps of hypothesis test→ PHANTOM
In the STAT list editor, enter the X data in list L1 and the Y data in list L2, paired so that the corresponding (x,y) values are next to each other in the lists.
On the STAT TESTS menu, scroll down with the cursor to select the LinRegTTest.
On the LinRegTTest input screen enter: Xlist: L1 ; Ylist: L2 ; Freq: 1
On the next line, at the prompt β or ρ, highlight "≠ 0" and press ENTER
Leave the line for "RegEq:" blank
Highlight Calculate and press ENTER.
The null and alternative hypotheses for GOF: may be written in sentences or may be stated as equations or inequalities.
Null hypothesis: The observed values of the data values and expected values are values you would expect to get.
Degrees of freedom GOF: Number of categories - 1
The goodness of fit is usually right-tailed
Large test statistic: Observed values and corresponding expected values are not close to each other.
Expected value rule: Needs to be above 5 to be able to use the test
Test of independence: Determines whether two factors are independent or not
The null hypothesis for independence: states that the factors are independent
The alternative hypothesis for independence: states that they are not independent (dependent).
Independence degrees of freedom: (number of columns -1)(number of rows - 1)
Expected value formula: (row total)(column total) / total number surveyed
Goodness-of-Fit: decides whether a population with an unknown distribution "fits" a known distribution.
Independence: decides whether two variables are independent or dependent. There will be two qualitative variables and a contingency table will be constructed.
Homogeneity: decides if two populations with unknown distributions have the same distribution as each other. There will be a single qualitative survey variable given to two different populations.
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