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katen-ka-za [31]
3 years ago
9

Researchers are studying rates of homeowners in a certain town. They believe that the proportion of people ages 36-50 who own ho

mes is signifificantly greater than the proportin of people age 21-35 who own homes and want to test this claim. The results of the surverys are: Homeowners Renters Total
Ages 21-35 18 38 56



Ages36-50 40 22 62


TOTAL 58 60 118



What are the null hypothesis and alternative hypothesis for this situation
Mathematics
1 answer:
Ira Lisetskai [31]3 years ago
6 0

Answer:

Being p1 the proportion for people of ages 36-50 and p2 the proportion for people of ages 21-35, the null and alternative hypothesis will be:

H_0: p_1-p_2=0\\\\H_a: p_1-p_2>0

Step-by-step explanation:

A hypothesis test on the difference of proportions needs to be performed for this case.

We have two sample proportions and we want to test if the true population proportions differ from each other, usign the information given by the sample statistics.

The claim is that the proportion of people of ages 36-50 who own homes is significantly greater than the proportin of people age 21-35 who own homes.

The term "higher" will define the alternative hypothesis, that is the hypothesis that represents what is claimed. The null hypothesis always include the equal sign, and will state that both proportions do not differ.

Being p1 the proportion for people of ages 36-50 and p2 the proportion for people of ages 21-35, the null and alternative hypothesis will be:

H_0: p_1-p_2=0\\\\H_a: p_1-p_2>0

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You are the operations manager of the Spartan Ice Cream Shoppe that produces its own ice cream. You make and sell five flavors;
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Answer:

(a) 90V + 75C + 70P + 55B + 40R

(b) - You can make up to 200 gallons

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10 ≤ V, C, P, B, R ≤ 75

(d) 75 gallons of Vanilla, 75 gallons of chocolate, 30 gallons of Pistachio, 10 gallons of Banana and 10 gallons of Rocky Road

Step-by-step explanation:

(a)Let V, C, P, B and R be the number of Vanilla, Chocolate, Pistachio, Banana and Rocky Road ice cream gallons you'd plan to make for the Spartan Ice Cream shop. The profit function would be

90V + 75C + 70P + 55B + 40R

And this is the formula that you are trying to optimize.

(b) The constraints are:

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(c) The constraint formula:

V + C + P + B + R ≤ 200

10 ≤ V, C, P, B, R ≤ 75

(d)  The solutions of this problem is, you would try to make as much as possible of the ones that generate the most profit, while keep an eyes on the constraints. Knowing this, you would

1. Make 10 gallons of each flavors, so a total of 50 gallons. That leaves you with 200 - 50 = 150 gallons left

2. Of the 150 gallons left, you make an extra 65 gallons for Vanilla (so a total of 75 Vanilla gallons). That leaves you with 150 - 65 = 85 gallons

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In the end, you should make: 75 gallons of Vanilla, 75 gallons of chocolate, 30 gallons of Pistachio, 10 gallons of Banana and 10 gallons of Rocky Road

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