Question

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), or U (uracil). The characters occur with different probabilities for each position. 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 there are 60 A’s in the 20th position.

Suppose that the probability of an "A" in the 20th position is 0.79 in ribosomal 5S RNA. Test the hypothesis that the new sequence is the same as ribosomal 5S RNA.

a) Write hypotheses. Explain why you should use a two sided alternative.

Answer 1

The null hypothesis is that the new sequence is the same as ribosomal 5S RNA, while the alternative hypothesis is that it is different. A two-sided alternative is used to test if the new sequence is significantly different or not from the ribosomal 5S RNA.

Step-by-step explanation:

In this scenario, the null hypothesis can be that the new sequence is the same as ribosomal 5S RNA, while the alternative hypothesis can be that the new sequence is different from ribosomal 5S RNA. It is important to use a two-sided alternative because we want to test whether the new sequence is either significantly different (has more or less A's) or not significantly different from the ribosomal 5S RNA.

To conduct this test, you would perform a two-sample t-test, where the null hypothesis would state that the mean number of A's in the 20th position for the new sequence is equal to the mean number of A's in the 20th position for ribosomal 5S RNA. The alternative hypothesis would state that the mean number of A's in the 20th position for the new sequence is not equal to the mean number of A's in the 20th position for ribosomal 5S RNA.