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.

What is the null hypothesis? What is the alternative hypothesis? What is the critical value? What is the standard error? What is the 95% confidence interval?