Question

a study compared weight loss between patients on diet a and patients on diet b. patients on diet a lost a mean of 7.6 pounds in six months, whereas patients on diet b lost a mean of 7.3 pounds in six months. suppose that the study was based on a sample of 400 patients on diet a and 400 patients on diet b, and the standard deviation of the amount lost was 3.6 pounds for diet a and 2.9 pounds for diet b. complete parts (a) through (d).
a. state the null and alternative hypotheses if you want to test whether the mean weight loss between the two diets is equal. what are the null and alternative hypotheses?
let \\( \mu _ { 1 } \\) represent the mean number of pounds patients on diet a lose in six months and \\( \mu _ { 2 } \\) represent the mean number of pounds patients on diet b lose in six months. choose the correct answer below
\\( \bigcirc \\) a. \\( h _ { 0 } : \mu _ { 1 } \geq \mu _ { 2 } \\)
\\( h _ { 1 } : \mu _ { 1 } < \mu _ { 2 } \\)
\\( \bigcirc \\) b. \\( h _ { 0 } : \mu _ { 1 } \leq \mu _ { 2 } \\)
\\( h _ { 1 } : \mu _ { 1 } > \mu _ { 2 } \\)
\\( \bigcirc \\) c. \\( h _ { 0 } : \mu _ { 1 } \
eq \mu _ { 2 } \\)
\\( h _ { 1 } : \mu _ { 1 } = \mu _ { 2 } \\)
\\( \bigcirc \\) d. \\( h _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \\)
\\( h _ { 1 } : \mu _ { 1 } \
eq \mu _ { 2 } \\)

Explanation:

The null hypothesis \(H_0\) is a statement of equality. Here, we want to test if the mean weight loss between the two diets is equal. So \(H_0:\mu_1 = \mu_2\). The alternative hypothesis \(H_1\) is the statement we are trying to find evidence for. Since we just want to test if they are not equal (a two - tailed test), \(H_1:\mu_1
eq\mu_2\).

Answer:

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