Biostat
A. Genetics
Ribosomal 5S RNA can be represented as a sequence of 120 nucleotides. Each nucleotide can be represented by one of four characters: A (adenine), G (guanine), C (cytosine), o U (uracil). The characters occur with different probabilities for each person. We wish to test if a new sequence is the same as ribosomal 5S RNA. For this purpose, we replicate the new sequence 100 times and find that there are 60 A’s in the 20th position. Use a 0.5 level of significance.
1. If the probability of an A in the 20th position is 0.79 in ribosomal 5S RNA, then test the hypothesis that the new sequence is the same as the ribosomal 5S RNA using the critical method.
2. Report a p-value corresponding to your results in the problem number 2.
B. Cancer
Suppose we identify fifty 50- to 54- year old women who have both a mother and sister with a history of breast cancer. Five of these women themselves have developed breast cancer at some time in their lives. If we assume that the expected prevalence rate of breast cancer in women whose mothers have had breast cancer is 4%, then does having a sister with the disease add to the risk?
C. Epidemiology
One hundred volunteers agree to participate in a clinical trial involving a dietary intervention. The investigators want to check how representative this sample is of the general population. One interesting finding is that 10 of the volunteers are current cigarette smokers. Use a 0.05 level of significance.
1. Assuming that 30% of the general population of adults are current smokers, state the hypothesis needed to test whether the volunteer group is representative of the general population regarding cigarette smoking.
Ho: The volunteer group is not a representative of the general population regarding cigarette smoking. (u =/= 30)Ha: The volunteer group is representative of the general population regarding cigarette smoking. (u=30)
2. Carry out the test described in C.1 and report a p-value. p-value: <0.0001. Since the
Ribosomal 5S RNA can be represented as a sequence of 120 nucleotides. Each nucleotide can be represented by one of four characters: A (adenine), G (guanine), C (cytosine), o U (uracil). The characters occur with different probabilities for each person. We wish to test if a new sequence is the same as ribosomal 5S RNA. For this purpose, we replicate the new sequence 100 times and find that there are 60 A’s in the 20th position. Use a 0.5 level of significance.
1. If the probability of an A in the 20th position is 0.79 in ribosomal 5S RNA, then test the hypothesis that the new sequence is the same as the ribosomal 5S RNA using the critical method.
2. Report a p-value corresponding to your results in the problem number 2.
B. Cancer
Suppose we identify fifty 50- to 54- year old women who have both a mother and sister with a history of breast cancer. Five of these women themselves have developed breast cancer at some time in their lives. If we assume that the expected prevalence rate of breast cancer in women whose mothers have had breast cancer is 4%, then does having a sister with the disease add to the risk?
C. Epidemiology
One hundred volunteers agree to participate in a clinical trial involving a dietary intervention. The investigators want to check how representative this sample is of the general population. One interesting finding is that 10 of the volunteers are current cigarette smokers. Use a 0.05 level of significance.
1. Assuming that 30% of the general population of adults are current smokers, state the hypothesis needed to test whether the volunteer group is representative of the general population regarding cigarette smoking.
Ho: The volunteer group is not a representative of the general population regarding cigarette smoking. (u =/= 30)Ha: The volunteer group is representative of the general population regarding cigarette smoking. (u=30)
2. Carry out the test described in C.1 and report a p-value. p-value: <0.0001. Since the