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Tutorial 5
Statistik inferensial 1. Stimasi 2. Uji hipotesis Mean proporsi variance uji hipotesis Tidak menolak Ho Menolak Ho
Ho benar 1-alpha
Ho salah Type II (beta)
Type error I (alpha)
1-beta (power) semakin tinggi power semakn bagus, yang mempengarhui power tinggi adalah n kecil.
Hypothesis Tests: I 1. The level of significance, alpha, is the probability of a. rejecting a false null hypothesis(1-beta) b. accepting a true null hypothesis(1-alpha) c. rejecting a true null hypothesis (alpha) d. accepting a false null hypothesis(beta) 2. If an investigator rejects the null hypothesis a. s/he has committed a Type II error b. s/he has committed a Type I error c. s/he has committed no error d. s/he may have committed a Type II error 1) a, b, and c 2) a and c 3) b and d 4) d only 5) none of the above 3. A Type II error is a. the probability that the null hypothesis is true b. the probability that the null hypothesis is false c. made if the null hypothesis is accepted when it is false d. made if the null hypothesis is rejected when it is true e. none of the above 4. The p-value is (peluang mengamati perbedaan sebesar yang kita amati, atau lebih besar, secra kebetulan jika Ho benar) P value < alpha tolak Ho menerima Ho P value ≥ alpha Cara mengambil keputusan : Statistik uji, Convidence Interval, P value
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Jika Uji normalitas Ho : data populasi normal H1 : data populasi tdk normal a. the probability of the null hypothesis being true b. the probability of the null hypothesis being false c. the probability of the test statistic or any more extreme results, assuming the null hypothesis is true d. the probability of the test statistic or any more extreme results, assuming the null hypothesis is false e. none of the above 5. A 95% confidence interval for the mean cholesterol level of adults over 65 years of age is (198, 208) mg/dl. The mean cholesterol level for adults 40-60 years of age i s 190 mg/dl. If a two-sided hypothesis test of Ho: μ=190 mg/dl were performed, we would: Diketahui: 95% convidence Interal (198-208) Uji hypothesis Ho µ = 190 mg/dl a. accept Ho at the 5% significance level b. reject Ho at the 5% significance level (karena CI (198-208)) c. accept Ho at the 1% significance level d. reject Ho at the 1% significance level e. can’t tell (karena diketahui 50-60, yg dintanyakn 65?????) 6. The 5% level of significance means: a. we’re taking a 5% risk of misstating the null hypothesis b. we’re taking a 5% risk that our sample is unrepresentative if the null hypothesis is true c. we’re taking a 5% risk of getting an unrepresentative sample if the alternative hypothesis is true d. we’re taking a 5% risk of making a wrong decision, regardless of which h ypothesis is true 7. Iron-deficiency anemia is an important nutritional health problem in Indonesia. A dietary assessment was performed in 51 children of 9 to 1 1 year-old males whose family were below the poverty line. The mean daily iron intake among these children was found to be 12.50 mg with a standard deviation of 4.75 mg. Suppose that the mean daily iron intake among a large population of 9-11 year-old boys from all income strata is 14.44 mg. We wish to test if the mean iron intake among the low-income boys is different from that of the boys in the general population. State the hypothesis that can be used to consider this question. 2 sisi (different) 1 sisi (bigger, larger, higher, smaller) one tailed, 2 tailed one sided 2 sided Ho : µ1=µ2 Ho : µ1≥µ2 Ho : µ1≤µ2 H1 : µ1≠µ2 H1 : µ1<µ2 H1 : µ1>µ2 Statsitik: nilai yg menggambarkan sampel Paramater : nilai yg menggambarkan populasi Diket: Xbar(rata” sampel) = 12,5 sampel S (sampel) = 4,47 sampel µ (rata” populasi)= 14,44 sampel a. H0: μ = 12.50 versus H1: μ 6=12.50 b. H0: μ = 14.44 versus H1: μ = 12.50
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c. H0: μ = 14.44 versus H1: μ < 14.40 d. H0: μ = 14.44 versus H1: μ 6=14.44 e. H0: μ < 14.44 versus H1: μ = 14.44 Hypothesis Tests II
1. A study was done to determine the effectiveness of an instruction booklet in improving nurses’ knowledge of testing for glycosuria in diabetes mellitus. A sample of 12 nurses was given a pretest prior to reading the booklet. After reading the booklet, the same nurses were given a post-test. Questions: a) State the null hypothesis for determining if the ins truction booklet was effective.????????? (1 sisi) Jawab : Ho = µ pre test < µ post test b) State the appropriate alternative hypothesis. Jawab : H1 = µ pre test < µ post test c) The appropriate t-statistic is: Paired t-test ( kebanyakan ada pre test dan post test, ada sampel yang sama, dan anak kembar) 2-sample t-test d) The degrees of freedom associated with this test statistic are: derajat bebas = n-1= 11
2. One method for assessing the effectiveness of a drug is to note its concentration in blood and/or urine samples at certain periods of time after giving the drug. Suppose we wish to compare the concentrations of two types of aspirin in urine specimens at one time and measure the 1-hour urine concentration. One week later, after the first aspirin has presumable been cleared from the system, we give the same dosage of the other aspirin to the same person and note the 1-hour urine concentration. Since the order of giving the drugs may affect the results, we use a table of random numbers to decide which of t he two types of aspirin to give first. We perform the experiment on 10 people. What statistical procedure would be appropriate for comparing the two types of aspirin? Jawab : the paired t test Karena sampel sama, (uji aspirin 1 dan uji aspirin 2) 3. A study was performed in 1086 to relate the use of oral contraceptives with the levels of various lipid fractions in a groups 163 non-pregnant, pre-menopausal women ages 21-39. The serum cholesterol among 66 current users of oral c ontraceptives was 201 + 37 (mg/dl) (Mean + Standard deviation), whereas for 97 nonusers it was 193 + 37 mg/dl. What statistical procedure would be appropriate for determining if cholesterol levels are affected by the oral contraceptive use? Jawab : the independent two-sample t test ( equal variance karena variansinya sama) Karena terdapat 2 kelompok berbeda tidak saling berkaitan User 66201+37 Non user 97 193+37 the independent two-sample t test (diuji), T test digunakan untuk sampel 1. Equal variansi 2. Unequal variansi Variansi opulasi (penjelasan) 1. Diketahui (Z test digunakan untuk populasi) 2. Tidak diketahui (T test digunakan untuk sampel) kemudian dianalisis apakah equal dan unequal
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4. In a pediatric clinic a study is carried out to see how effective aspirin is in reducing temperature. Twelve 5-year-old girls suffering from influenza had their temperatures taken immediately before and 1 hour after administration of aspirin. W hat is the appropriate statistical procedure for determining if aspirin is reducing the temperature? State the appropriate null and alternative hypothesis Jawab : Menurunkan Temperatur Ho : temp1 ≤ tempt2 H1 : tmpt 1 > tempt2 5. An investigator wishes to determine if sitting upright in a chair versus lying down on a bed will affect a person’s blood pressure. The investigator decides to use each of 10 patients as his or her own control and collects systolic blood pressure d ata in both the sitting and lying positions. What statistical procedure would be appropriate to determine the effect of position on blood pressure? Jawab : The paired T Test sampel sama Hypothesis Test III 1. A clinical trial was designed to test a drug that was believed to decrease bloodclotting time. Forty subjects were selected and randomized to yield two groups, each with n=20. One group was given the drug and the other group was given a placebo, and served as a control. The mean clotting time, given in minutes, for the drug treatment group is 4.90 minutes with variance of 10.24 minutes squared. The mean clotting time for the control group is 7.45 and the variance is 12.96 minutes squared. Question: State the null hypothesis to test differences between the treatment and control groups. Jawab : Ho: µ drug=µ placebo State the appropriate alternative hypothesis. Jawab : Ha : µ drug ≠ µ placebo Using the above results, set up the appropriate test. (In stata) Diketahui Treatment obat Xbar : 4,9 S2 : 0,24 Control placebo Xbar : 7,45 S2 : 12,96
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Display = ttesti 20 4.9 3.2 20 7.45 3.6 Two-sample t test with equal variances -----------------------------------------------------------------------------| Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+-------------------------------------------------------------------x| 20 4.9 .7155418 3.2 3.402354 6.397646 y| 20 7.45 .8049845 3.6 5.765148 9.134852 ---------+-------------------------------------------------------------------combined | 40 6.175 .5694267 3.601371 5.023226 7.326774 ---------+-------------------------------------------------------------------diff | -2.55 1.077033 -4.730339 -.3696608 -----------------------------------------------------------------------------diff = mean(x) - mean(y) t = -2.3676 Ho: diff = 0 degrees of freedom = 38 Ha: diff < 0 Pr(T < t) = 0.0115
Ha: diff != 0 Pr(|T| > |t|) = 0.0231
Ha: diff > 0 Pr(T > t) = 0.9885
Jadi Ho : 0,0231 < 0,05,.. Jadi Ho ditolak artinya ada perbedaan antara pemberian obat dengan tidak pemebrian obat. 2. A class experiment in pharmacology consisted of dist ributing packets of instant coffee to students. The contents of the packet were to be mixed with hot water and drank shortly before bedtime. The student received packets on two occasions: one time the packet contained a placebo and the other time it contained coffee with caffeine. Among other measurements, the students took their pulse rates (in beats per minute) before consuming the instant coffee or placebo and then again afterward. The students were classified as to whether they were coffee drinkers (those who usually consumed two cups or more per day) or non-coffee drinkers (those who usually consumed one or fewer cups per day). The results for 65 non-coffee drinkers and 85 coffee drinkers are given below: 65 Non-Coffe Drinkers 85 Coffe Drinkers Caffein Placebo Caffein Placebo N 50 15 44 41 Mean 4.1 0.9 4.9 2 Questions: a) State the null and alternative hypothesis for determining if the response is the same among Coffee Drinkers. Jawab : µ caffein = µ placebo µ cafein ≠ µ placebo b) What is the appropriate statistical procedure to test the null hypothesis in (a)? Jawab : The Independent two-sample t test Sampel berbeda c) What are the degrees of freedom associated with the test statistic in (b)? Jawab : n1+n2-2 44+41-2 = 83
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d)
State the null and alternative hypotheses to determine if the caffeine response is the same between Non-Coffee and Coffee Drinkers. e) What is the appropriate statistic procedure to test the null hypothesis in (d)? The independent two-sample t test f) What are the degrees of freedom associated with the test statistic in (e)? Jawab : n1+n2-2 50+44-2 = 92 3. A recent study attempted to compare the working environment in offices w here smoking was permitted with that in offices where smoking was not permitted. Measurements were made of carbon monoxide (CO) at 1:20 pm in 40 work areas. Where smoking was permitted, the mean CO=11.6 parts per million (ppm) and the standard deviation CO=7.3 ppm. Where smoking was banned, the mean CO=6.9 ppm and the standard deviation CO=2.7 ppm. What statistical procedure would be appropriate to see whether or not the mean CO is different in the two types of working environments? Bebeda atau tidak?? Jawab : the independent two sample t test Boleh rokok Xbar: 11.6 S : 7,3 Rokok dilarang Xbar : 6,9 S : 2,7 (In stata) #Display = sdtesti 20 . 7.3 20 . 2.7 Variance ratio test -----------------------------------------------------------------------------| Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+-------------------------------------------------------------------x| 20 . 1.63233 7.3 . . y| 20 . .6037384 2.7 . . ---------+-------------------------------------------------------------------combined | 40 . . . . . -----------------------------------------------------------------------------ratio = sd(x) / sd(y) f = 7.3100 Ho: ratio = 1 degrees of freedom = 19, 19 Ha: ratio < 1 Pr(F < f) = 1.0000
Ha: ratio != 1 2*Pr(F > f) = 0.0001
Ha: ratio > 1 Pr(F > f) = 0.0000
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#Display = ttesti 20 11.6 7.3 20 6.9 2.7, unequal Two-sample t test with unequal variances -----------------------------------------------------------------------------| Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+-------------------------------------------------------------------x| 20 11.6 1.63233 7.3 8.183495 15.01651 y| 20 6.9 .6037384 2.7 5.636361 8.163639 ---------+-------------------------------------------------------------------combined | 40 9.25 .9377824 5.931057 7.353156 11.14684 ---------+-------------------------------------------------------------------diff | 4.7 1.740402 1.108797 8.291203 -----------------------------------------------------------------------------diff = mean(x) - mean(y) t = 2.7005 Ho: diff = 0 Satterthwaite's degrees of freedom = 24.1029 Ha: diff < 0 Pr(T < t) = 0.9938
Ha: diff != 0 Pr(|T| > |t|) = 0.0125
Ha: diff > 0 Pr(T > t) = 0.0062
Jadi Ho : 0,0062 < 0,05,.. Jadi Ho ditolak artinya ada perbedaan antara.........dengan..................
