Question

a magazine claims that the mean amount spent by a customer at burger stop is greater than the a customer at fry world. the results for samples of customer transactions for the two fast food res below. at α = 0.05, can you support the magazine’s claim? assume the population variances are e samples are random and independent, and the populations are normally distributed. complete pa below.

burger stop | fry world
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\\(\bar{x}_1 = \\$9.89\\) | \\(\bar{x}_2 = \\$9.26\\)
\\(s_1 = \\$0.79\\) | \\(s_2 = \\$0.68\\)
\\(n_1 = 13\\) | \\(n_2 = 11\\)

(a) partially visible

a. \the mean amount spent by a customer at burger stop is equal to the mean amount spe fry world.\

b. \the mean amount at burger stop is greater than the mean amount at fry world.\

c. \the mean amount at fry world is greater than the mean amount s burger stop.\

d. \the mean amount fry world.\

what are \\(h_0\\) and \\(h_a\\)?

the null hypothesis, \\(h_0\\), is dropdown the alternative hypothesis, \\(h_a\\), is dropdown

options for hypotheses: \\(\mu_1 = \mu_2\\), \\(\mu_1 \leq \mu_2\\), \\(\mu_1 \geq \mu_2\\)

Explanation:

Step1: Define Hypotheses

The magazine claims the mean at Burger Stop ($\mu_1$) is greater than at Fry World ($\mu_2$). The null hypothesis ($H_0$) is the opposite of the claim or a statement of equality. So $H_0: \mu_1 \leq \mu_2$. The alternative hypothesis ($H_a$) is the claim, so $H_a: \mu_1 > \mu_2$.

Step2: Match with Options

From the dropdowns, the null hypothesis should be $\mu_1 \leq \mu_2$ (matching the statement "The mean amount at Burger Stop is less than or equal to at Fry World" or the mathematical form $\mu_1 \leq \mu_2$), and the alternative is $\mu_1 > \mu_2$ (matching "The mean amount at Burger Stop is greater than at Fry World").

Answer:

The null hypothesis, $H_0$, is $\boldsymbol{\mu_1 \leq \mu_2}$ (or the statement "The mean amount spent by a customer at Burger Stop is less than or equal to the mean amount spent at Fry World").
The alternative hypothesis, $H_a$, is $\boldsymbol{\mu_1 > \mu_2}$ (or the statement "The mean amount spent by a customer at Burger Stop is greater than the mean amount spent at Fry World").