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Hypothesis Testing

Hypothesis Testing. Writing Conclusions. Statistically Significant. An event is considered to be statistically significant if it is so rare that it probably wouldn’t just happen by chance.

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Hypothesis Testing

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  1. Hypothesis Testing Writing Conclusions

  2. Statistically Significant An event is considered to be statistically significant if it is so rare that it probably wouldn’t just happen by chance.

  3. Ex 1: An interview you saw online states that 291 out of 500 people they interviewed answered yes when they were asked if gun control laws should be enforced more strictly. Does this imply that a majority of those interviewed believe that gun control laws should change?

  4. Ex 1: An interview you saw online states that 291 out of 500 people they interviewed answered yes when they were asked if gun control laws should be enforced more strictly. Step 1: Write a Null and Alternative Hypothesis. p = .5 (There isn’t a majority who believes) p > .5 (A majority believes in an increase in gun laws)

  5. Ex 1: An interview you saw online states that 291 out of 500 people they interviewed answered yes when they were asked if gun control laws should be enforced more strictly. p = .5 (There isn’t a majority who believes) p > .5 (A majority believes in an increase in gun laws) Step 2: Find the z-score.

  6. Ex 1: An interview you saw online states that 291 out of 500 people they interviewed answered yes when they were asked if gun control laws should be enforced more strictly. p = .5 (There isn’t a majority who believes) p > .5 (A majority believes in an increase in gun laws) Step 3: Find the p-value. =.9999 P(>3.73) = 1 -.9999 = .0001

  7. Significance Level The significance level is abreviated with the symbol α. The most commonly used level is α = .05 (α = .01 and α = .10 are also used) If the p-value is smaller then α, it is said to be so unlikely that we must conclude that the Null Hypothesis is false (this event is statistically significant).

  8. Significance Level There are only two conclusions to be made: If p-value < α: Reject There is sufficient evidence to state the Alt. Hypothesis is true. If p-value > α: Fail to reject There is insufficient evidence to conclude that the Alt. Hypothesis is true.

  9. Ex 1: An interview you saw online states that 291 out of 500 people they interviewed answered yes when they were asked if gun control laws should be enforced more strictly. p = .5 (There isn’t a majority who believes) p > .5 (A majority believes in an increase in gun laws) Step 4: Make conclusions. p - value= .0001

  10. Ex 1: An interview you saw online states that 291 out of 500 people they interviewed answered yes when they were asked if gun control laws should be enforced more strictly. p = .5 (There isn’t a majority who believes) p > .5 (A majority believes in an increase in gun laws) Step 4: Make some conclusions. p - value= .0001 Since p-value = .0001 < .05 there is sufficient evidence to reject the null hypothesis and conclude that a majority of people believe that gun control laws should be enforced more strictly.

  11. Steps for Hypothesis Tests for p

  12. Ex 2: A study is performed to examine how many people enjoy watching Saturday Night Live in 2005. 90 of the 402 people interviewed state that they watch the show regularly. A similar study done a few years earlier stated that 25% of the population watched regularly. Does this mean that less people watched SNL in 2005? Step 1: Write a Null and Alternative Hypothesis. p = .25 (25% watch) p < .25 (less then 25% watch)

  13. Ex 2: A study is performed to examine how many people enjoy watching Saturday Night Live in 2005. 90 of the 402 people interviewed state that they watch the show regularly. A similar study done a few years earlier stated that 25% of the population watched regularly. Does this mean that less people watched SNL in 2005? p = .25 (25% watch) p < .25 (less then 25% watch) Step 2: Find the z-score.

  14. Ex 2: A study is performed to examine how many people enjoy watching Saturday Nigh Live in 2005. 90 of the 402 people interviewed state that they watch the show regularly. A similar study done a few years earlier stated that 25% of the population watched regularly. Does this mean that less people watched SNL in 2005? p = .25 (25% watch) p < .25 (less then 25% watch) Step 3: Find the p-value. p-value = .119

  15. Ex 2: A study is performed to examine how many people enjoy watching Saturday Nigh Live in 2005. 90 of the 402 people interviewed state that they watch the show regularly. A similar study done a few years earlier stated that 25% of the population watched regularly. Does this mean that less people watched SNL in 2005? p = .25 (25% watch) p < .25 (less then 25% watch) Step 4: Make a conclusion. p-value = .119 Since .119 > .05, we fail to reject the null Hypt. There is insufficient evidence to conclude that less people watch SNL.

  16. Hypothesis Testing 2 Sided Tests

  17. Ex 1: An online magazine bragged that 64% of all Americans still buy CDs. In 2000, it was said that ¾ of all Americans bought CDs. Does this mean the proportion of CD buyers has changed? Step 1: Write a Null and Alternative Hypothesis. p = .75 (75% buy) p .75 (Some other proportion buys CDs)

  18. Ex 1: An online magazine bragged that 64% of Americans still buy CDs (Taken from an SRS of 100). In 2000, it was said that ¾ of all Americans bought CDs. Does this mean the proportion of CD buyers has changed? p = .75 (75% buy) p .75 (Some other proportion buys CDs) Step 2: Find the z-score.

  19. Ex 1: An online magazine bragged that 64% of Americans still buy CDs (Taken from an SRS of 100). In 2000, it was said that ¾ of all Americans bought CDs. Does this mean the proportion of CD buyers has changed? p = .75 (75% buy) p .75 (Some other proportion buys CDs) Step 3: Find the p-value. normalcdf(-E99,-2.54) = .0055 p-value = 2 x .0055 = .011

  20. Ex 1: An online magazine bragged that 64% of Americans still buy CDs (Taken from an SRS of 1,000). In 2000, it was said that ¾ of all Americans bought CDs. Does this mean the proportion of CD buyers has changed? p = .75 (75% buy) p .75 (Some other proportion buys CDs) Step 3: Find the p-value. p-value = .011 Since .011 < .05, there is sufficient evidence to reject the Null Hyp. We can conclude that the proportion of people who buy CDs in not .75 .

  21. Finding the p-value for 2 sided tests: If the z-score is positive: *Find the upper tail probability then mult. by 2. If the z-score is negative: *Find the lower tail probability then mult. by 2.

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