Mathematics, 08.04.2020 17:37 reaperqueen21

In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant, it is found that 63 of 100 urban residents favor the construction while only 59 of 125 suburban residents are in favor. We wish to know if there a significant difference between the proportions of urban and suburban residents who favor construction of the nuclear plant. Do the step by step procedure on hypothesis test of two proportions, use 0.05 level.

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The proportion of suburban residents who favor construction of the nuclear plant is 16% lower than that of those urban residents with the same criteria.

Since in a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant, it is found that 63 of 100 urban residents favor the construction while only 59 of 125 suburban residents are in favor, to determine if there is a significant difference between the proportions of urban and suburban residents who favor construction of the nuclear plant, the following calculation must be performed:

63/100 = 0.63 59/125 = 0.47 0.63 - 0.47 = 0.16

Therefore, the proportion of suburban residents who favor construction of the nuclear plant is 16% lower than that of those urban residents with the same criteria.

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Answer from: kdawg203

The test statistic z = z = 2.368 >1.97 (at 5% level of significance)

we rejected null hypothesis at 5% level of significance

There is significant difference between the proportions of urban and suburban residents who favor construction of the nuclear plant.

Step-by-step explanation:

Given data In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant, it is found that 63 of 100 urban residents

The first sample proportion $p₁ = \frac{63}{100} =0.63$

The construction of 59 of 125 suburban residents are in favor

The second sample proportion $p_{2} = \frac{59}{125} = 0.472$

Given the sample sizes are n₁ = 100 and n₂ =125

Null hypothesis(H₀):-there is no significant difference between the proportions of urban and suburban residents who favor construction of the nuclear plant.

Alternative hypothesis: H₁

There is significant difference between the proportions of urban and suburban residents who favor construction of the nuclear plant.

Level of significance:-

∝ =0.05

Tabulated value z=1.96

Test statistic

$z = \frac{p_{1}-p_{2} }{\sqrt{pq(\frac{1}{n_{1} } +\frac{1}{n_{2} } )} }$

where $p = \frac{n_{1}p_{1} +n_{2}p_{2} }{n_{1} +n_{2} }$ q = 1- p

Substitute all values in above equation

$p = \frac{100X0.63+0.472X125}{100+125} = 0.542$

q = 1-p = 1 - 0.542 = 0.458

The test statistic

$z = \frac{0.63-0.472}{\sqrt{0.542X0.458}(\frac{1}{100}+\frac{1}{125} )}$

on simplification , we get

z = 2.368 >1.97 (at 5% level of significance)

we rejected null hypothesis at 5% level of significance

Conclusion:-

There is significant difference between the proportions of urban and suburban residents who favor construction of the nuclear plant.

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