Question

a fast food restaurant estimates that the mean sodium content in one of its breakfast sandwiches is no more than 912 milligrams. a random sample of 30 breakfast sandwiches has a mean sodium content of 901 milligrams. assume the population standard deviation is 18 milligrams. at \\( \alpha = 0.10 \\), do you have enough evidence to reject the restaurants claim? complete parts (a) through (e). (a) identify the null hypothesis and alternative hypothesis. \\( \bigcirc \mathrm { a } \\). \\( h _ { 0 } : \mu \leq 901 \\) \\( h _ { a } : \mu < 901 \\) (claim) \\( \bigcirc \mathrm { b } \\). \\( h _ { 0 } : \mu \
eq 912 \\) (claim) \\( h _ { a } : \mu = 912 \\) \\( \bigcirc \mathrm { c } \\). \\( h _ { 0 } : \mu > 912 \\) \\( h _ { a } : \mu \leq 912 \\) (claim) \\( \bigcirc \mathrm { d } \\). \\( h _ { 0 } : \mu = 901 \\) (claim) \\( h _ { a } : \mu \
eq 901 \\) \\( \bigcirc \mathrm { e } \\). \\( h _ { 0 } : \mu \leq 912 \\) (claim) \\( h _ { a } : \mu > 912 \\) \\( \bigcirc \mathrm { f } \\). \\( h _ { 0 } : \mu < 901 \\) (claim) \\( h _ { a } : \mu \geq 901 \\)

Explanation:

The null hypothesis \(H_0\) is the statement being tested. The restaurant claims that the mean sodium content \(\mu\) is no more than \(912\) milligrams, so \(H_0:\mu\leq912\) (this is the claim). The alternative hypothesis \(H_a\) is the statement that we are trying to find evidence for. Since we want to check if there is enough evidence to reject the claim (that \(\mu\leq912\)), the alternative hypothesis is \(H_a:\mu > 912\).

Answer:

E. \(H_0:\mu\leq912\) (claim), \(H_a:\mu > 912\)