Hypothesis Testing: One Sample t-Test

Table 2 Critical Values of t: The t-Table (Note: Values of -1= values of +to.) Two-Tailed Test One-Tailed Test crit 0 +crit 0 Alpha Level Alpha Level df a = .05 0 = .01 df C = .05 0 =.01 12.706 63.657 4.303 6.314 31.821 9.925 3.182 2.920 6.965 5.841 2.776 2.353 4.541 4.604 YOUAWN- 2.132 2.571 3.747 4.032 2.447 2.015 3.365 3.707 2.365 1.943 3.143 3.499 2.306 1.895 2.998 3.355 1.860 2.896 2.262 3.250 1.833 2.228 2.821 3.169 10 1.812 2.764 2.201 3.106 11 1.796 2.718 2.179 3.055 12 2.160 1.782 2.681 3.012 13 1.771 2.650 2.145 2.977 14 1.761 2.624 2.131 2.947 15 1.753 2.602 2.120 2.921 16 1.746 2.583 2.110 2.898 17 1.740 2.567 2.101 2.878 18 1.734 2.552 2.093 2.861 19 1.729 2.539. 2.086 2.845 20 1.725 2.528 21 2.080 2.831 21 1.721 2.518 22 2.074 2.819 22 1.717 2.508 23 2.069 2.807 23 1.714 2.500 24 2.064 2.797 24 1.711 2.492 25 2.060 2.787 25 1.708 2.485 26 2.056 2.779 26 1.706 2.479 27 2.052 2.771 27 1.703 2.473 28 2.048 2.763 28 1.701 2.467 29 2.045 2.756 29 1.699 2.462 30 2.042 2.750 30 1.697 2.457 40 1.684 2.423 40 2.021 2.704 2.660 60 1.671 2.390 60 2.000 1.980 2.617 120 1.658 2.358 120 1,960 2.576 1.645 2.326 From Table 12 of E. Pearson and H. Hartley, Biometrike Tables for Statisticians, Vol. 1, 3rd ed. (Cambridge: Cambridge University Press, 1966.) Reprinted with the permission of the Biometrika Trustees.One Sample t-TEST HYPOTHESIS STEP Create either the two-tailed or one-tailed Ha and H. (Experimental and statistical hypotheses) ONE Two-tailed One-Tailed (H) Hail >_(H) Hou = _(H) How = _(H) SAMPLING DISTRIBUTION STEP Set up the sampling t-distribution and do not assume a normal distribution until df > 120 TWO Select oc Locate region of rejection Determine critical value --use df=N- 1 to find terit in the t-table COMPUTE OBTAINED VALUE STEP Compute tobe THREE X - H tobty N 2 N- 1 INTERPRET AND REPORT RESULTS STEP Compare tobe to terit. If tobe is beyond terit the results are significant. If toatis not beyond terit FOUR the results are non-significant If significant compute confidence interval (Sx)(-terit) + XS H S (5x)(+ terit) + X Report the results Significant results Non significant results t(df) = tobe , p <.05 t tobt p> .05HYPOTHESIS STEP Create either the two-tailed or one-tailed Ha and Ho (Experimental and statistical hypotheses) ONE Two-tailed One-Tailed (H Hail > ( H) HOW= - (H) Hous _(H) SAMPLING DISTRIBUTION STEP Set up the sampling t-distribution and do not assume a normal distribution until df > 120 TWO Select oc Locate region of rejection Determine critical value --use df=N- 1 to find torit in the t-table COMPUTE OBTAINED VALUE STEP Compute tobt THREE X - H tobe ST= N- 1 INTERPRET AND REPORT RESULTS STEP Compare tobe to terit. If tobe is beyond tort the results are significant. If tearis not beyond terit FOUR the results are non-significant If significant compute confidence interval (Sx) (-terit ) + X H = (5x)(+ terit) + X Report the results Significant results Non significant results t(df) = tobe , p <.05 t tobe p> .05ONE SAMPLE t-Test exercise: Pushups-comparing female college students average to female national average. The average number of pushups a 20 year old woman can do is 25 so # = 25. Does not report standard deviation. Question: how do female college students compare to the national average for 20 year old women? Give test to a sample to female college students. Use their * to estimate the u for the national population. Then compare the u for college student sample to the u of 25 for the national average for women. If female college students score differently from the female national population then found relationship in which as status in college changes then the number of pushups one can do changes. (Data comes from students in a previous STAT200 class.) Female Number of X2 College pushups (X) Student Participants 1 2 60 3 12 4 15 5 40 6 0 7 30 8 50 9 25 10 10 11 15 N= EX= EX'= X =TWO Select OC Locate region of rejection Determine critical value --use df=N- 1 to find tori in the t-table COMPUTE OBTAINED VALUE STEP Compute tobt THREE X - tobe Ex S,= N N- 1 INTERPRET AND REPORT RESULTS STEP Compare tobe to terit. If tobe is beyond teris the results are significant. If tabris not beyond teris FOUR the results are non-significant If significant compute confidence interval (5x ) ( -terit ) + X S H S (5x)(+ terie) + X Report the results Significant results Non significant results t(df) = tobe , p <.05 t tobe p> .05ONE SAMPLE lTest exercise: Pushupsoompa ring MALE college students average to MALE national average. The average number of pushups a 20 year old MAN can do is 44 so 11 = 44. Does not report standard deviation. Question: How do MALE college students compare to the national average for MEN? Give test to a sample of male college students. Use their X to estimate the u for the national population of college males. Then con'Ipare the u for college students to the u for all men. If college students score differently from the MALE national AVERAGE then found relationship in which as status in college changes then the number of push ups one can do changes. (Data comes from students in a previous STATZOO class.) Male Number of College pushups [x] Student Partlcl- ants One Sam le t-TEST HYPOTHESIS STEP Create either the two-tailed or oneAtailed h"1 and H9 {Experimental and statistical hypotheses] 0N E Twotailed OneTailed Hall at _lul Hana >_lul Hn=u= _IllI Ha=u_lul SAMPLING DISTRIBUTION STEP Set up the sampling tdistribu'tion and do not assume a normal distribution until (If 3- 120 ONE SAMPLE t-Test exercise: Television watching Americans spend 34 hours a week watching live television according to Neilson numbers so # = 34. Does not report standard deviation. Question: how do college students compare to this national average? Give test to a sample to college students. Use their X to estimate the u for the national population. Then compare the u for college students to the u of 34 for the national population. If college students score differently from the national population then found relationship in which as you select out college students then amount of TV watching changes. (Data comes from students in a previous STAT200 class.) College Hours watching X2 Student television (X) Participants 1 NEW NO HOOP N= EX= EX2= (EX)= X =