ACTIVITY SET 13 March 24 Stat 200 Sections 4 6 Activity 13 1 a An instructor asked students to randomly choose one of the numbers 1 2 3 4 5 6 7 With random picking the chance of picking the number 1 is 1 7 The instructor believes that students will pick the number 3 more often than would occur by random picking In words what are null and alternative hypotheses for the instructor Null hypothesis Alternative hypothesis Express the hypotheses in statistical notation H 0 Ha 1 2b The maker of M Ms candy claims that 10 of all M Ms are red Ralph thinks otherwise he believes the percent is less than 10 In words what are null and alternative hypotheses for Ralph Null hypothesis Alternative hypothesis Express the hypotheses in statistical notation H 0 Ha Next week we ll focus on testing hypotheses about means Here are symbols for either one mean or the difference between two means like difference between mean GPAs of men and women Parameter of interest One mean Difference between means of two independent groups Symbol 1 2 c A medical researcher wants to demonstrate that the mean body temperature for healthy people is in fact less than the commonly accepted value of 98 6 Fahrenheit In words what are null and alternative hypotheses for the researcher Null hypothesis Alternative hypothesis Express the hypotheses in statistical notation H 0 Ha d We want to show that the mean scores on a memory test will be different for women group 1 and men group 2 In words what are null and alternative hypotheses in this situation Null hypothesis Alternative hypothesis Express the hypotheses in statistical notation H 0 Ha Activity 13 2 DEFINITIONS A type 1 error occurs if we incorrectly pick the alternative hypothesis pick it when null is really the truth A type 2 error occurs if we incorrectly pick the null hypothesis pick it when the alternative is really the truth a Refer back to parts b about M Ms of Activity 13 1 Explain what the type 1 and type 2 errors are in this situation Do this in terms of the real world situation b Refer back to parts d about memory of men and women of Activity 13 1 Explain what the type 1 and type 2 errors are in this situation Do this in terms of the real world situation Activity 13 3 p p 0 p 0 1 p 0 This measures the n difference between the sample p and the null hypothesis value p0 The bottom of the test statistic is a standard error computed using the null hypothesis value In each case calculate the value of the test statistic z and show work When testing hypotheses about a proportion the test statistic is a In a clinical trial of a treatment for a psychiatric problem the proportion of successful treatments is 72 with n 200 patients participating Hypotheses are null p 65 and alternative p 65 b In a sample of n 400 M Ms there are 28 red candies Hypotheses are null p 10 and alternative p 10 with p population proportion that is red c In a taste test 63 of 100 tasters prefer Cola A over Cola B We re testing null p 50 versus alternative p 50 where p population proportion that prefers Cola A d In a poll 80 of 160 U S adults say they approve of the president s job performance We re testing null p 50 versus alternative p 50 where p population proportion approving of the president Activity 13 4 When testing hypotheses about a population proportion the rules for using the normal curve to find a p value are Symbol in Ha less than greater than not equal What to do Find the probability less than z Find the probability greater than z Find the probability less than the negative version of z then multiply by 2 Use either Table A 1 in the book or Minitab s Calc Probability Distributions Normal to help you find p values for each of the situations in Activity 13 3 a Find p value for part a of activity 13 3and draw a sketch showing the region b Find p value for part b of activity 13 3 and draw a sketch showing the region c Find p value for part c of activity 13 3 and draw a sketch showing the region d Find p value for part d of activity 13 3 and draw a sketch showing the region Activity 13 5 Refer to activities 13 3 and 13 4 For each part indicate whether the null or the alternative should be picked a b c d