VCU STAT 210 - Test 6 Practice Test #1 (3 pages)

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Test 6 Practice Test #1



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Test 6 Practice Test #1

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3
School:
Virginia Commonwealth University
Course:
Stat 210 - Basic Practice of Statistics
Basic Practice of Statistics Documents
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Test 6 Practice Test 1 Lymphoma is a cancer in the lymphatic cells of the immune system Typically lymphomas present as a solid tumor of lymphoid cells Treatment might involve chemotherapy and in some cases radiotherapy and or bone marrow transplantation and can be curable depending on the histology type and stage of the disease These malignant cells often originate in lymph nodes presenting as an enlargement of the node a tumor There are many types of lymphomas and in turn lymphomas are a part of the broad group of diseases called hematological neoplasms 1 One category of lymphoma is non Hodgkin lymphoma which is the classification of many different types Of interest is to estimate the mean survival time in years of a patient diagnosed with non Hodgkin lymphoma For this problem only assume that the standard deviation of the survival times for all patients diagnosed with non Hodgkin lymphoma is 9 2 years What is the minimum number of non Hodgkin lymphoma patients that would need to be selected to allow the calculation of a 95 confidence interval with margin of error no greater than 3 5 years Please circle your final answer 2 A simple random sample of 51 non Hodgkin lymphoma patients was selected and their survival time from initial diagnosis to death was determined for each The mean survival time for this sample of 51 patients was 17 8 years with a standard deviation of 4 6 years and the distribution was heavily skewed to the right since a few patients had lived many years between initial diagnosis and death If appropriate use this information to calculate and interpret a 95 confidence For questions 3 and 4 the answer choices for both multiple choice questions are as follows A The margin of error would increase and the width would decrease B The margin of error would decrease and the width would increase C Neither the margin of error nor the width would be affected D Both the margin of error and the width would increase E Both the margin of error and the width would decrease 3 In question 2 a confidence interval was computed based on a sample of 51 patients If the number of patients in the sample were decreased to 41 what impact would this have on the margin of error and width of the confidence interval 4 In question 2 a 95 confidence interval was computed If the confidence level were increased from 95 to 99 confidence what impact would this have on the margin of error and the width of the confidence interval 5 If diagnosed early lymphoma is often curable and it is usually diagnosed in older people and not the young Suppose that the ages of patients when diagnosed with lymphoma are skewed heavily to the left since diagnosis in the young is rare with a mean of 61 years of age and a standard deviation of 10 4 years of age If a simple random sample of 64 lymphoma patients is selected and the age of each at diagnosis recorded describe completely the sampling distribution of resulting mean age at diagnosis of this sample of 64 lymphoma patients X the 6 For patients diagnosed with non Hodgkin lymphoma it is known that most patients diagnosed are older and hence the distribution of the ages of patients when diagnosed with non Hodgkin lymphoma is skewed heavily to the left However the mean age at diagnosis of all people diagnosed with non Hodgkin lymphoma is not known It is conjectured that this mean age is 55 years and researchers want to test this versus the alternative that the mean age at diagnosis of all people diagnosed with non Hodgkin lymphoma is different from 55 years State the appropriate null and alternative hypotheses that should be tested 7 Consider all the information in question 6 and assume that the standard deviation of the ages at diagnosis for all people diagnosed with non Hodgkin lymphoma is 10 4 years To test the hypotheses in question 6 data for the 12 patients most recently diagnosed with non Hodgkin lymphoma at VCU MCV Hospitals was recorded The mean age of these 12 patients was 58 75 years If appropriate use this information to test the hypotheses stated in question 6 at the 05 level of significance 8 Consider the three statements below Draw a circle around any if any and all that are valid statistical hypotheses H A X 16 H0 19 2 HA 97 9 Definition the probability assuming the null hypothesis is true that a test statistic takes a value as extreme or more extreme than the value actually observed is which of the following A Significance level B Margin of error C Test statistic D P value E Point estimate 10 What is the point estimate of the population mean A 0 B Z C X D t E s 11 If a low grade lymphoma is becoming symptomatic radiotherapy or chemotherapy are the treatments of choice although they do not cure the lymphoma they can alleviate the symptoms particularly painful lymphadenopathy Patients with these types of lymphoma can live near normal lifespans but the disease is incurable Treatment of some other more aggressive forms of lymphoma can result in a cure in the majority of cases but the prognosis for patients with a poor response to therapy is worse Treatment for these types of lymphoma typically consists of aggressive chemotherapy For patients treated with chemotherapy of interest is the mean number of days between the first and last treatment It is conjectured that the mean number of days between the first and last chemotherapy treatment is 42 days and of interest is to test this conjecture versus the alternative that the mean number of days between the first and last chemotherapy treatment is less than 42 days State the appropriate null and alternative hypotheses that should be tested 12 Consider the information and hypotheses specified in question 11 A simple random sample of 28 lymphoma patients is selected and the number of days between the first and last chemotherapy treatment was recorded for each The mean for this sample of 28 observations was 38 25 days the standard deviation for this sample of 28 observations was 7 75 and the distribution of the data was fairly symmetrical If appropriate use this information to test the hypotheses stated in question 11 at the 10 level of significance TEST 6 Practice Test 1 Solutions Z 2 1 960 9 2 m 3 5 2 5 152 2 26 54 Round up to 27 patients 1 n 2 We have a simple random sample and the sample size is large enough for the Central Limit Theorem to apply n 51 40 so the assumptions are satisfied The population standard deviation is unknown so we must use the tdistribution 95 CI implies t 50 2 009 So X t 50 sn 17 8 2


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