Question

Problem #1:

(a) Suppose that we identify 169 women 50 to 54 years of age who have both a mother and a sister with a history of breast cancer. 17 of these women themselves have developed breast cancer at some time in their lives. If we assume that the proportion of breast cancer cases in women whose mothers have had breast cancer is 8%, does having a sister with the disease increase the risk? Find the p-value. (b) At the 1% significance level, what is the conclusion of the above hypothesis test? (A) We cannot conclude that having a sister with the disease increases the risk since the p-value is greater or equal to .02 (B) We conclude that having a sister with the disease increases the risk since the p-value is less than 0.01 (C) We conclude that having a sister with the disease increases the risk since the p-value is less than .02 (D) We cannot conclude that having a sister with the disease increases the risk since the p-value is greater or equal to 0.01 (E) We cannot conclude that having a sister with the disease increases the risk since the p-value is less than 0.01 (F) We conclude that having a sister with the disease increases the risk since the p-value is greater than or equal to 0.01 (G) We cannot conclude that having a sister with the disease increases the risk since the p-value is less than .02 (H) We conclude that having a sister with the disease increases the risk since the p-value is greater than or equal to .02 (c) A genetic model suggests that 80% of plants grown from a cross between two given strains of seeds will be of the dwarf variety. After breeding a sample of these plants, 154 were observed to be of the dwarf variety. Suppose that we do a hypothesis test to see if the sample results strongly contradict the genetic model and find the p-value to be 0.0139. What is the meaning of this p-value ? (A) If the genetic model is not correct, it is very unlikely (probability 0.0139) to obtain exactly 154 plants of the dwarf variety in the given sample. (B) If the genetic model is correct, it is very unlikely (probability 0.0139) to obtain exactly 154 plants of the dwarf variety in the given sample. (C) If the genetic model is not correct, it is very unlikely (probability 0.0139) to obtain 154 or more plants of the dwarf variety in the given sample. (D) The p-value of 0.0139 is the probability of making a Type II error. (E) The p-value of 0.0139 is the probability of making a Type I error. (F) The p-value of 0.0139 is the probability of making a wrong decision. (G) If the genetic model is correct, it is very unlikely (probability 0.0139) to obtain 154 or more plants of the dwarf variety in the given sample.

Answer 1

1a)

from above p value =0.1619 (please try 0.1611 if this comes wrong)

b)

since p value >0.010

D) We cannot conclude that having a sister with the disease increases the risk
since the p-value is greater or equal to 0.01

c)

. (G) If the genetic model is correct, it is very unlikely (probability 0.0139) to obtain
154 or more plants of the dwarf variety in the given sample.