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For questions 1 through 6, please refer to the following information: Studies have shown that low vitamin D is associated with impaired fertility, endometriosis, and polycystic ovary syndrome. Vitamin D regulates the antimullerian hormone (AMH), follicle-stimulating hormone, mRNA, and expression of genes in reproductive tissues, implicating a role in female reproduction. Lata et al. conducted a prospective study to compare AMH levels in infertile and fertile females with vitamin D deficiency. Among the 35 fertile females (group 1), the mean AMH level was 3.47 with a standard deviation of 2.59. Among the 35 infertile females (group 2), the mean AMH level was 1.94 with a standard deviation of 1.30. Assuming the variances are unequal and a 0.05 significance level, use the confidence interval method to test the claim that infertile females have different AMH levels compared to fertile females. To do so, answer each of the following questions.

1. What is the null hypothesis (H0)? (1 point) a. ?1 - u2 = 0 b. ?1 - u2 ? 0 c. ?1 = u2 d. ?? 1 - ?? 2 =0 e. ?? 1 = ?? 2 f. Both a and c are correct g. Both d and e are correct

2. What is the alternative hypothesis? (1 point) a. ?1 - u2 = 0 b. ?1 - u2 ?0 c. ?1 ? u2 d. ?? 1 - ?? 2 ?0 e. ?? 1 ? ?? 2 f. Both b and c are correct g. Both d and e are correct

3. What is the critical value? (1 point) a. 1.691 b. 1.668 c. 1.995 d. 2.032

4. What is the standard error? (1 point) a. 0.11 b. 0.33 c. 0.49 d. 0.99

5. What is the 95% confidence interval? Provide an appropriate interpretation of this confidence interval. (1 point) a. There is a 95% chance that the true mean difference in AMI levels will fall within the interval (0.53, 2.53) when comparing fertile females to infertile females. b. There is a 95% chance that the true mean difference in AMI levels will fall within the interval (0.70, 2.35) when comparing fertile females to infertile females. c. We are 95% confident that the interval (0.53, 2.53) actually does contain the true mean difference in AMI levels when comparing fertile females to infertile females. d. We are 95% confidence that the interval (0.70, 2.35) actually does contain the true mean difference in AMI levels when comparing fertile females to infertile females. e. Both a and c are correct f. Both b and d are correct

6. What conclusion should you make regarding the null hypothesis? (2 points) a. Because the interval does not include 0, reject the H0 due to sufficient evidence and conclude that fertile females have a different mean AMI level compared to infertile females. b. Because the interval does not include 1, reject the H0 due to sufficient evidence and conclude that fertile females have a different mean AMI level compared to infertile females. c. Because the interval does not include 3.47, reject the H0 due to sufficient evidence and conclude that fertile females have a different mean AMI level compared to infertile females. d. Because the interval does not include 0, fail to reject the H0 due to insufficient evidence and conclude that fertile females do not have a different mean AMI level compared to infertile females. e. Because the interval does not include 1, fail to reject the H0 due to insufficient evidence and conclude that fertile females do not have a different mean AMI level compared to infertile females. f. Because the interval does not include 3.47, fail to reject the H0 due to insufficient evidence and conclude that fertile females do not have a different mean AMI level compared to infertile females

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