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Understanding Hypothesis Testing: Assumptions and Probabilities

Hypothesis testing is a fundamental statistical method for making informed decisions based on assumptions. One key assumption is the hypothesis itself, which is tested by calculating the probability of observed outcomes given that hypothesis. For example, in coin tossing, we assume that the probability of heads is ½. By examining various toss possibilities, we can determine if observed results deviate significantly from expected outcomes. Similarly, in card drawing, if we assume every card is equally likely, the probability of correctly naming a drawn card is 1/52. This approach helps in validating or rejecting hypotheses.

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Understanding Hypothesis Testing: Assumptions and Probabilities

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  1. Hypothesis testing Make assumptions. One of them is the “hypothesis.” Calculate the probability of what happened based on the assumptions. If the probability of what happened is too low, reject the hypothesis.

  2. Coin • Assumption: The probability of heads is ½. • One toss possibilities: • The assumption implies that each possibility is equally likely.

  3. Coin • Assumption: The probability of heads is ½. • Two toss possibilities: • The assumption implies that each possibility is equally likely.

  4. Three toss possibilities (each 1/8 =.125):

  5. Four toss possibilities (each 1/16 = .0625):

  6. Five toss possibilities (each hypothesized to have probability of 1/32 = .03125):

  7. If hypothesis is true that heads and tails are equally likely heads

  8. Six tosses possibilities, each hypothesized to have a probability of 1/64 = .015625:

  9. Cards

  10. The probability of correctly naming a card drawn at random is

  11. The probability of correctly naming a card drawn at random is 1/52 • … if you hypothesize that every card is equally likely to be drawn

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