Statistics: Unlocking the Power of Data Lock 5 Section 4.1 Introducing Hypothesis Tests

Statistics: Unlocking the Power of Data Lock 5 Review A 99% confidence interval is a) wider than a 95% confidence interval b) narrower than a 95% confidence interval c) the same width as a 95% confidence interval A 99% CI contains the middle 99% of bootstrap statistics, while a 95% CI contains only the middle 95%. To be more confident that the interval contains the truth, a 99% interval has to contain more values than a 95% interval.

Statistics: Unlocking the Power of Data Lock 5 Extrasensory Perception Is there such a thing as extrasensory perception (ESP) or a “sixth sense”? Do you believe in ESP? a) Yes b) No

Statistics: Unlocking the Power of Data Lock 5 Extrasensory Perception There are five cards with five different symbols If there is no such thing as ESP, what proportion of guesses should be correct? a) p = 0 b) p = 1/4 c) p = 1/5 d) p = 1/2 Because there are 5 cards, each person has a 1/5 chance of guessing correctly each time, if ESP does not exist.

Statistics: Unlocking the Power of Data Lock 5 Statistical Evidence 0.7 is the highest, so provides the strongest evidence of ESP.

Statistics: Unlocking the Power of Data Lock 5 Sleep versus Caffeine Mednick, Cai, Kanady, and Drummond (2008). “Comparing the benefits of caffeine, naps and placebo on verbal, motor and perceptual memory,” Behavioral Brain Research, 193, Students were given words to memorize, then randomly assigned to take either a 90 min nap, or a caffeine pill. 2 ½ hours later, they were tested on their recall ability. Explanatory variable: sleep or caffeine Response variable: number of words recalled Is sleep or caffeine better for memory?

Statistics: Unlocking the Power of Data Lock 5 Sleep versus Caffeine What is the parameter of interest in the sleep versus caffeine experiment? a) Proportion b) Difference in proportions c) Mean d) Difference in means e) Correlation The response variable (number of words recalled) is quantitative and the explanatory variable (sleep or caffeine) is categorical, so we are interested in a difference in means.

Statistics: Unlocking the Power of Data Lock 5 Sleep versus Caffeine Let  s and  c be the mean number of words recalled after sleeping and after caffeine. Is there a difference in average word recall between sleep and caffeine? What are the null and alternative hypotheses? a) H 0 :  s ≠  c, H a :  s =  c b) H 0 :  s =  c, H a :  s ≠  c c) H 0 :  s ≠  c, H a :  s >  c d) H 0 :  s =  c, H a :  s >  c e) H 0 :  s =  c, H a :  s <  c The null hypotheses is “no difference,” or that the means are equal. The alternative hypothesis is that there is a difference.

Statistics: Unlocking the Power of Data Lock 5 State Hypotheses What are the null and alternative hypotheses to determine whether there is evidence that the proportion of people who support gun control differs between males and females? a) H 0 : p m = p f vs H a : p m < p f b) H 0 :  m =  f vs H a :  m <  f c) H 0 : p m = p f vs H a : p m  p f d) H 0 :  m ≠  f vs H a :  m >  f e) H 0 : p m  p f vs H a : p m = p f The null hypotheses is “no difference,” or that the means are equal. The alternative hypothesis is that there is a difference.

Statistics: Unlocking the Power of Data Lock 5 State Hypotheses What are the null and alternative hypotheses to determine whether there is evidence that the average number of hours of sleep per night for college students is less than 7? We always use the population parameter in hypotheses. The null hypotheses is always “equals”, and the alternative hypothesis is what we are seeking evidence of: in this case, that the mean is less than 7.

Statistics: Unlocking the Power of Data Lock 5 Sleep versus Caffeine a) there is a difference between sleep and caffeine for memory (and data show sleep is better) b) there is not a difference between sleep and caffeine for memory c) nothing

Statistics: Unlocking the Power of Data Lock 5 Hours of Sleep per Night In testing whether the mean number of hours of sleep per night, , for college students is less than 7, we have H 0 :  = 7 vs H a :  < 7 If the results of the test are statistically significant, we can conclude… a) There is evidence that the mean is equal to 7. b) There is evidence that the mean is less than 7. c) There is evidence that the mean is greater than 7. d) There is no evidence of anything. e) College students get lots of sleep.

Statistics: Unlocking the Power of Data Lock 5 Hours of Sleep per Night In testing whether the mean number of hours of sleep per night, , for college students is less than 7, we have H 0 :  = 7 vs H a :  < 7 If the results of the test are not statistically significant, we can conclude… a) There is evidence that the mean is equal to 7. b) There is evidence that the mean is less than 7. c) There is evidence that the mean is greater than 7. d) There is no evidence of anything. e) College students get lots of sleep.