Mathematics, 23.05.2020 07:00 SimplyGenesis762

Two opposing opinions were shown to a random sample of 1,744 US buyers of a particular political news app. The opinions, shown in a random order to each buyer, were as follows: Opinion A: Prescription drug regulation is more important than border security. Opinion B: Border security is more important than prescription drug regulation. Buyers were to choose the opinion that most closely reflected their own. If they felt neutral on the topics, they were to choose a third option of "Neutral." The outcomes were as follows: 30% chose Opinion A, 64% chose Opinion B, and 6% chose "Neutral." Part A: Create and interpret a 95% confidence interval for the proportion of all US buyers who would have chosen Opinion A. (5 points) Part B: The number of buyers that chose Opinion A and the number of buyers that did not choose Opinion A are both greater than 10. Why must this inference condition be met? (5 points)

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Answer from: robbylynnbonner

95% confidence interval for the proportion of all US buyers who would have chosen Opinion A is [0.28 , 0.32].

Step-by-step explanation:

We are given that Two opposing opinions were shown to a random sample of 1,744 US buyers of a particular political news app.

The outcomes were as follows: 30% chose Opinion A, 64% chose Opinion B, and 6% chose "Neutral."

Firstly, the Pivotal quantity for 95% confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of US buyers who chose Opinion A = 0.30

n = sample of US buyers = 1,744

p = population proportion

Here for constructing 95% confidence interval we have used One-sample z test for proportions.

(a) SO, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level

of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

95% confidence interval for p = [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.30-1.96 \times {\sqrt{\frac{0.30(1-0.30)}{1,744} } }$ , $0.30+1.96 \times {\sqrt{\frac{0.30(1-0.30)}{1,744} } }$ ]

= [0.28 , 0.32]

Therefore, 95% confidence interval for the proportion of all US buyers who would have chosen Opinion A is [0.28 , 0.32].

(b) The number of buyers that chose Opinion A and the number of buyers that did not choose Opinion A are both greater than 10, that is;

Number of buyers that did chose Opinion A = $n \times p$

= $1,744 \times 0.30$ = 523.2

Number of buyers that did not chose Opinion A = $n \times (1-p)$

= $1,744 \times 0.70$ = 1220.8

Now, this inference condition should have been met because if these were not met then we were not able to use the normal distribution statistics above because binomial distribution can be converted to normal distribution only when and n(1-p) both are greater than 10.

Answer from: Quest

The slope best fit isc. 1/6 mile per hour
What is the slope of the line of best-fit? a. 6 miles per hourb. 12 miles per hourc. 1/6 miles per h

Answer from: Quest

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc

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