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Restaurateur Denny Valentine is evaluating two sites, Raymondville and Rosenberg, for his next restaurant. He wants to prove that Raymondville residents (population 1) dine out more often than Rosenberg residents (population 2). Denny commissions a market survey to test this hypothesis. The market researcher used a random sample of X families from each suburb, and reported the following:

1 = X times per month and 2 = X times per month. Assume that σ1 = 2 and σ2 = 3. With α = .01, the appropriate decision is:_________

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Answer:

Step-by-step explanation:

From the information given:

let [tex]\mu_1[/tex] be the men of the population 1 (Raymondville) and [tex]\mu_2[/tex] be the mean of the population 2 (Rosenberg).

Here the Restaurateur wants to prove that Raymondville residents dine out more often than Rosenberg residents.

i.e [tex]\mu_1 > \mu _2[/tex]

The null hypothesis and alternative hypothesis:

[tex]H_o : \mu_1 \le \mu_2 \\ \\ H_a: \mu_1 > \mu_2[/tex]

[tex]H_o : \mu_1 \le \mu_2\ \ vs \ \ H_a: \mu_1 > \mu_2 \implies \text{upper tailed test}[/tex]

The shows that this test is one-tailed with the rejection area on the right side.

The appropriate decision: is to reject [tex]\mathbf{H_o}[/tex] if the test statistics is greater than the critical value)

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