7.23-7.25 Genetics: Ribosomal 5S RNA can be represented as a sequence of 120 nuc

Question

7.23-7.25 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), or U (uracil). The characters occur with different probabilities for each position. We wish to test whether 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.

7.23 What will be the result if we conclude that the mean is greater than 45 if the actual mean is 45?

i. We have made a type I error.

ii. We have made a type II error.

iii. We have made the correct decision.

7.24 What will be the result if we conclude that the mean is 45 when the actual mean is 50?

i. We have made a type I error.

ii. We have made a type II error.

iii. We have made the correct decision.

7.25 Which of the following sample results yields the smallest p-value and why?

i. x = 28, s = 6

ii. x = 27, s = 6

iii. x = 32, s = 2

iv. x = 26, s = 9

Explanation / Answer

7.23

As we incorrectly rejected Ho, we made a

OPTION I: TYPE I ERROR [ANSWER]

*************************

7.24

As we incorrectly failed to reject Ho, we made a

OPTION II: TYPE II ERROR [ANSWER]

*************************

7.25

The P value gets smaller if the absolute value of z gets larger.

As z = (X-u0)*Sqrt(n)/s

and n = 100, u0 = 45, then

OPTION I: z = -28.33333333
OPTION II: z = -30
OPTION III: z = -65
OPTION IV: z = -21.11111111

Hence,

OPTION III: X = 32, s = 2 [ANSWER]

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