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For questions 14-17, refer to the following information: In one study of 63 women with the BRCA1 variant, 26 were diagnosed with breast cancer by age 70. Use a 0.01 significance level to test the claim that among women with the BRCA1 variant, that less than half (or less than 50%) are diagnosed with breast cancer by age 70. To test the hypothesis, you'll need to answer the following

Questions. 14. What is the null hypothesis (H0)? (1 point)

a. = 0.50

b. < 0.50

c. 0.50

d. = 0.50

e. < 0.50

f. 0.50

15. What is the alternative hypothesis (H1)? (1 point)

a. = 0.50

b. < 0.50

c. 0.50

d. = 0.50

e. < 0.50

f. 0.50

16. What is the value of the test statistic you should use to test the given hypothesis? (1 point)

a. -2.175

b. -2.82

c. -1.38

d. 1.65

e. 0.12

17. If the p-value (corresponding to your test statistic) is 0.0838, what conclusion should you make? (2 points)

a. Because p > 0.01, fail to reject the null hypothesis due to insufficient evidence and conclude that at least half of women with the BRCA1 variant are diagnosed with breast cancer by age 70.

b. Because p > 0.05, fail to reject the null hypothesis due to insufficient evidence and conclude that at least half of women with the BRCA1 variant are diagnosed with breast cancer by age 70.

c. Because p > 0.05, reject the null hypothesis due to sufficient evidence and conclude that less than half of women with the BRCA1 variant are diagnosed with breast cancer by age 70.

d. Because p > 0.01, reject the null hypothesis due to sufficient evidence and conclude that less than half of women with the BRCA1 variant are diagnosed with breast cancer by age 70.