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##### AMS 110 Pretest D Assignment

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Question;SHOW ALL WORK, ENTER ANSWERS ON THE BLANK PROVIDEDNameSB ID #:__ Your TAThis is worth 5% of your final exam grade. Please print and hand in this original document with your work onit. Show all work in any blank space provided on each page and enter your final answer on the blank lineprovided. You may check your work with a calculator, but all computations must be shown.1. (14 points) A school administrator wants to compare two reading methods: Method S andmethod B. A class of 44 students is randomly divided into two groups of 22 each. One is taughtwith method S and the other is taught with B. Is the mean reading score with S higher than withB? The sample mean reading score for method S was 43.0691, with a standard deviation of5.5641 and the sample mean reading score for method B was 40.0768 with a standarddeviation of 5.2247. These are sample standard deviations. No alpha is provided for thisproblem.State the null and the alternate hypotheses Ho:versus Ha: ____________Assume that the data are independent samples from normal populations with equal populationvariances. Thus, we perform a pooled variance t test.Find an estimate of the pooled variance. ______________(4 decimal places)Find sp (3 decimals) ____________________Degrees of Freedom = ______________The critical value(s) from the t table at the appropriate degrees of freedom are given by____________________The t test statistic is ______________Estimate the p-value______________State and interpret your decision:____________________________________________________________________________________________________________________________________________________________________________________________________________________________________Previously, you were asked to perform a pooled variance t-test.Were we justified in assuming equal variances? To answer this question please conduct ahypothesis test (F test) to check for equality of variances.State the null and alternate hypothesesHo: ___________________versus Ha: ______________________State the F test statistic _________________________The numerator and denominator degrees of freedom______,_____State the critical value obtained from the F table ____________(F table is posted under Lectures on Blackboard for your convenience.)State your conclusion of this F test. Were we justified in conducting apooled variance t test?__________________________________________________________________________________________________________(Yes/NO)If the pooled variance t test is not warranted, (i.e. if variances are not the same), what test is onesupposed to use to compare the means?______________________________________________________________TOTAL POINTS FOR #1________2. (11 points) David wants to compute whether an alternate route to work would be quicker. For thenext 58 working days he randomly divides his observations into two groups of 29 days each.He drives the first route for one set of 29 days and drives the second for the other set of 29days recording, for each day, the commuting times in minutes. Assume that times ofcommute are normal.Route 1n=29sample mean = 31.945s=5.87Route 2n=29sample mean = 28.105s=6.24a.Does the assumption of common population standard deviation seem plausible?State the null and alternate hypotheses Ho:b.versusHa:_____________The numerator and denominator degrees of freedom______,______c.Give the test statistic_________________d.What is your decision regarding common variance______________________________________________________________________________________________________________________________________e.State the hypothesis to test if route two is quicker than route one.Ho:Ha:_________________________f. The test statistic is ____g. The p-value ish. The degrees of freedom are_______________i. The decision is __________________________________________________________Route 2 (does/does not) appear to be quicker.j. State the F critical value from the F table that was used in part d____________k.State the pooled variance__________________TOTAL POINTS FOR #2________3. (13 points) We would like to compare the characteristics of tuberculosis meningitis in patientsinfected with HIV and those who are not infected. In particular, we would like to determine whetherthe two populations have the same mean age. A sample of 37 infected patients has mean age 27.9years and a standard deviation 5.6 years. A sample of 19 patients who are not infected has meanage 38.8 years and standard deviation 21.7 years. Alpha =.05Conduct a hypothesis test to check for equality of variances.State the null and alternate hypothesesHo___________________versus Ha:__________Compute the F test statistic ___________State the numerator and denominator deg of freedom______,_____State the critical value obtained from the F table ____________State your conclusion regarding the variances._____________________________________________________________________________________________________________________________________________________________________Based on (a), what test will you use to determine if the 2 populations have the same meanage?_______________________________________________________We continue with the test on the next page:State Ho: ______________________ versusHa: ______________________Find the test statistic __________________State the degrees of freedom (Welch/Satterthwaite)_____________State the critical value(s) _____________State your conclusion, and justify your conclusion using the critical values and the test statistic._____________________________________________________________________________________________________________________________________________________________________Approximate the P-value for this test. ______________________State the confidence interval for the difference in means________,________TOTAL POINTS FOR #3________4. (18 points) Company officials were concerned about the length of time a particular drug productretained its potency. A random sample of n1 = 10 bottles of the product was drawn from theproduction line and analyzed for potency. A second sample of n2 = 10 bottles was obtained andstored in a regulated environment for 1 year. Let 1 denote the mean potency for all bottlescoming off the production line and let 2 denote the mean potency for all bottles retained for aperiod of 1 year. Assume that population variances are unknown but equal. Is the potency forfresh drugs different from that for stored drugs? Use alpha =.05Potency Reading for the two samples:Fresh: 10.2 10.510.3Stored: 9.89.69.7Ho = ____________10.89.59.810.110.69.610.710.210.29.81010.110.69.9Ha = ____________Find the sample mean for fresh bottles____________(2 decimal places)Find the sample mean for stored bottles__________(2 decimal places)Find the sample standard deviation, s1 for fresh bottles_________(4 decimal places)Find the sample standard deviation, s2 for stored bottles________(4 decimal places)Compute the 95% confidence interval for 1 - 2 _____________Find an estimate of the pooled variance. ______________(4 decimal places)Find sp (3 decimals) ____________________ Degreesof Freedom = ______________the critical values from the t table at the appropriate degrees of freedom are given by____________________The t test statistic is ______________Estimate the p-value______________State and interpret your decision: ______________________________________________In this problem you were asked to perform a pooled variance t-test. Were we justified inassuming equal variances? To answer this question, conduct a hypothesis test (F test) to checkfor equality of variances.State the null and alternate hypothesesHo:Ha: ________State the F test statistic _________________________The numerator and denominator deg of freedom, ____State the critical value obtained from the F table ____________(F table is posted under Lectures on Blackboard for your convenience.)State your conclusion of this F test. Were we justified in conducting apooled variance t test?___________________________________________________________________________________________________________________________________________________________________________________________________________________(Yes/NO)TOTAL POINTS FOR #4________5. (9 points) Consider the paired data shown here:Pair12345X2128172427Y2930212533DifferenceIn order to test whether the means are equal or not, a t test is performed at alpha = 1%.a. Ho:versusHa: ____________b. The mean of the differences = ___________c. Standard deviation of the differences = _________(4 decimal places)d. Degrees of freedom = ____________e. t test statistic = _____________f.Critical value(s) for this test = ____________g. Decision: ____________________________h. Estimate the P-value_______________i. Appropriate confidence interval for the difference in means: (________, _______)TOTAL POINTS FOR #5________6. (7 points) From a socio-demographic Risk factors in spousal abuse study, it is observed that thedistribution of ages in a sample is as follows:AgeNumber in sample20-2410325-3421635-44171TotalConduct a chi-square goodness of fit at the 10 % significance level to test whether the sampleprovides a good match to the known age distribution in the population. The known percentages are18%, 50%, 32%Ho:versusHa: ____________The expected number in each category is_,, _______Which group above seems to be underrepresented in the sample?_____________The chi-squared test statistic is ________________The critical value from the chi-squared table is _____________The p-value is ___________Will you reject Ho? Explain in the context of the problem___________________________________________________________________________________________________________________________________________TOTAL POINTS FOR #6________7. (8 points) Sample data has been collected in a study of calcium supplements and their effects onblood pressure. A placebo group and a calcium group began the study with blood pressuremeasurements. The sample values are listed below. At the.05 significance level, test the claim thatthe two sample groups come from populations with the same standard deviation.Placebo: 124.6104.896.5116.3106.1128.8107.2123.1118.1108.5120.4122.5123.4102.7118.1114.7120.9104.4116.3109.6127.7108124.3106.6121.4113.2113.6Calcium: 129.1Find the sample standard deviation, for Placebo_________(4 decimal places)Find the sample standard deviation, for Calcium_________(4 decimal places)State the null and alternate hypothesesHo:Ha: ________Find the test statisticFind the critical valueState the appropriate degrees of freedomDraw the appropriate distribution showing the proper critical value. Label all necessary components.What is your conclusion? Explain

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