Test 6 Practice Test #1Lymphoma is a cancer in the lymphatic cells of the immune system. Typically, lymphomas present as a solid tumor oflymphoid cells. Treatment might involve chemotherapy and in some cases radiotherapy and/or bone marrowtransplantation, and can be curable depending on the histology, type, and stage of the disease. These malignant cellsoften originate in lymph nodes, presenting as an enlargement of the node (a tumor). There are many types oflymphomas, 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 isto estimate = the mean survival time, in years, of a patient diagnosed with non-Hodgkin lymphoma. For this problemonly, assume that the standard deviation of the survival times for all patients diagnosed with non-Hodgkin lymphoma is9.2 years. What is the minimum number of non-Hodgkin lymphoma patients that would need to be selected to allow thecalculation 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 initialdiagnosis to death, was determined for each. The mean survival time for this sample of 51 patients was 17.8 years with astandard deviation of 4.6 years, and the distribution was heavily skewed to the right since a few patients had lived manyyears 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 inthe sample were decreased to 41, what impact would this have on the margin of error and width of the confidenceinterval?_____ 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 thatthe 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 lymphomapatients is selected and the age of each at diagnosis recorded, describe completely the sampling distribution of ¯X, theresulting mean age at diagnosis of this sample of 64 lymphoma patients.6. For patients diagnosed with non-Hodgkin lymphoma it is known that most patients diagnosed are older and hence thedistribution 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 thatthis mean age is 55 years, and researchers want to test this versus the alternative that the mean age at diagnosis of allpeople diagnosed with non-Hodgkin lymphoma is different from 55 years. State the appropriate null and alternativehypotheses 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 peoplediagnosed with non-Hodgkin lymphoma is 10.4 years. To test the hypotheses in question 6, data for the 12 patients mostrecently diagnosed with non-Hodgkin lymphoma at VCU-MCV Hospitals was recorded. The mean age of these 12patients was 58.75 years. If appropriate, use this information to test the hypotheses stated in question 6 at the = .05level of significance.8. Consider the three statements below. Draw a circle around any (if any) and all that are valid statistical hypotheses.HA: ¯X ≠16H0: = 19.2 HA: > 97_____ 9. Definition: the probability, assuming the null hypothesis is true, that a test statistic takes a value as extreme ormore 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) s11. If a low-grade lymphoma is becoming symptomatic, radiotherapy or chemotherapy are the treatments of choice; althoughthey do not cure the lymphoma, they can alleviate the symptoms, particularly painful lymphadenopathy. Patients withthese types of lymphoma can live near-normal lifespans, but the disease is incurable. Treatment of some other, moreaggressive, forms of lymphoma can result in a cure in the majority of cases, but the prognosis for patients with a poorresponse to therapy is worse. Treatment for these types of lymphoma typically consists of aggressive chemotherapy. Forpatients treated with chemotherapy, of interest is = the mean number of days between the first and last treatment. It isconjectured that the mean number of days between the first and last chemotherapy treatment is 42 days, and of interest isto test this conjecture versus the alternative that the mean number of days between the first and last chemotherapytreatment 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 isselected and the number of days between the first and last chemotherapy treatment was recorded for each. The mean forthis sample of 28 observations was 38.25 days, the standard deviation for this sample of 28 observations was 7.75, andthe distribution of the data was fairly symmetrical. If appropriate, use this information to test the hypotheses stated inquestion 11 at the = .10 level of significance.TEST 6 Practice Test #1 Solutions1. n
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