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Hypothesis Testing about Proportions part 1

Hypothesis Testing about Proportions part 1. Hypothesis statements One and Two tailed tests. Vocab : 1A. Hypothesis Test: A test to determine if your sample suggests the population is different than what you originally thought.

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Hypothesis Testing about Proportions part 1

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  1. Hypothesis Testing about Proportions part 1 Hypothesis statements One and Two tailed tests

  2. Vocab: 1A Hypothesis Test: A test to determine if your sample suggests the population is different than what you originally thought Could my sample have come from a population with this proportion? P The normal population

  3. Vocab: 2A Assumptions for Hypothesis Test of proportion: Independence of events Random sample or representative Sample less than 10% Success/Fail at least 10 each P The normal population

  4. Vocab: 3A Null Hypothesis: the claim being tested, “no change from the normal”, “no difference”, the status quo, or what is historically expected. Ho The normal population

  5. Alternate Hypothesis: What we should conclude if the Ho is unlikely, plausible values for the proportion if the null is rejected, what we think maybe the proportion is, if the status quo is wrong what is the proportion, Vocab: 4A & 5A Ha  Ho Ha > Ho Ha < Ho What my sample says the population is. Ha is the new mean based on my sample but because of the ME my sample might just be normal variableness around the Ho H0 H0 H0 Ha Ha Ha Ha

  6. Vocab: 6A Ho and C.I. (paired together) If the Ha falls in a C.I. based on your critical value than the Ha is just the normal variableness of sampling. Samples vary – fail to reject the Ho Can’t accept Ho because other samples might fall outside the C.I.

  7. Vocab: 6A Ho and C.I. (paired together) But if the Ha falls outside a C.I. based on your critical value, than the Ha replaces the Ho as the population proportion until another sample comes along that says different. This sample couldn’t have reasonably come from the population – reject the Ho

  8. Vocab: 7A Ha > Ho P-Values (a decimal number that is a probability) What is the probability that we would see this sample come from the population of the Null Hypothesis Ha The P-Value is the probability of seeing data like these given that Ho is true. H0

  9. P-Values (When Am I Surprised?) The smaller the p-value the less likely it was sample variableness

  10. Would it surprise you if the chance was 12% ? P-Values (the measure of surprise) 88% 12% 0.12 The smaller the p-value the less likely it was sample variableness

  11. Would it surprise you if the chance was 5% ? P-Values (the measure of surprise) 95% 5% 0.05 0.05 The smaller the p-value the less likely it was sample variableness

  12. Would it surprise you if the chance was 2.5% ? P-Values (Am I Surprised?) 95% 2.5% 2.5% 0.025 0.025 The smaller the p-value the less likely it was sample variableness

  13. Would it surprise you if the chance was 0.6% ? P-Values (Am I Surprised?) 99.4% 0.006% 0.006 The smaller the p-value the less likely it was sample variableness

  14. Not Surprised Surprised ! P-Values (a two tail test vs one tail) 95% 5% 0.05 The smaller the p-value the less likely it was sample variableness

  15. Not Surprised Surprised ! Surprised ! P-Values (a two tail test vs one tail) 95% 2.5% 2.5% 0.025 0.025 The smaller the p-value the less likely it was sample variableness

  16. Example #1 • There are supposed to be 20% orange M&Ms. Suppose a bag of 122 has only 21 orange ones. Does this contradict the company's 20% claim? Assumptions: Hypothesis Statement: Null Hypothesis: Alternate Hypothesis: Critical value: Pg 1.2 – assumptions Pg 1.3 – P and p-hat Pg 1.4 – null and alternative hyp Pg 1.5 – one or two tail Pg 1.6 – critical value at 95%

  17. Example #2 • A 1996 report from the U.S. Consumer Product Safety Commission claimed that at least 90% of all American homes have at least one smoke detector. A city's fire department has been running a public safety campaign about smoke detectors consisting of posters, billboards, and ads on radio and TV and in the newspaper. The city wonders if this concerted effort has raised the local level above the 90% national rate. Building inspectors visit 400 randomly selected homes and find that 376 have smoke detectors. Find Assumptions: Hypothesis Statement: Null Hypothesis: Alternate Hypothesis: Critical value: Pg 1.2 – assumptions Pg 1.3 – P and p-hat Pg 1.4 – null and alternative hyp Pg 1.5 – one or two tail Pg 1.6 – critical value at 95%

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