Question

given in the table are the bmi statistics for random samples of men and women. assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. complete parts (a) and (b) below. use a 0.05 significance level for both parts.

a. test the claim that males and females have the same mean body mass index (bmi).

what are the null and alternative hypotheses?

○ a. ( h_{0}: mu_{1}=mu_{2} )
( h_{1}: mu_{1}<mu_{2} )
○ b. ( h_{0}: mu_{1}=mu_{2} )
( h_{1}: mu_{1}>mu_{2} )
○ c. ( h_{0}: mu_{1}
eq mu_{2} )
( h_{1}: mu_{1}<mu_{2} )
○ d. ( h_{0}: mu_{1}=mu_{2} )
( h_{1}: mu_{1}
eq mu_{2} )

Explanation:

Step1: Understand the null hypothesis concept

The null hypothesis \(H_0\) is a statement of equality. In a test for the equality of two population means \(\mu_1\) and \(\mu_2\) (claiming the same mean BMI for males and females), the null hypothesis is \(H_0:\mu_1 = \mu_2\).

Step2: Understand the alternative hypothesis concept

The alternative hypothesis \(H_1\) is the statement we test against the null. Since we are just testing if the means are different (not specifying a direction like greater than or less than), the alternative hypothesis is \(H_1:\mu_1
eq\mu_2\)

Answer:

D. \(H_0:\mu_1=\mu_2\), \(H_1:\mu_1
eq\mu_2\)