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kolbaska11 [484]
3 years ago
11

QUESTION 3 Toyota provides an option of a sunroof and side airbag package for its Corolla model. This package costs $1400. Assum

e that prior to offering this option package, Toyota wants to determine the percentage of Corolla buyers who would pay $1400 extra for the sunroof and side airbags. How many Corolla buyers must be surveyed if we want to be 95% confident that the sample percentage is within four percentage points of the true percent all Corolla buyers
Mathematics
1 answer:
Orlov [11]3 years ago
6 0

Answer:

n=601

Step-by-step explanation:

Formula used:

n=z(\frac{\alpha }{2})^2\frac{p(1-p) }{E^2}

Solution:

n=z(\frac{\alpha }{2})^2\frac{p(1-p) }{E^2}

Where,

\frac{\alpha }{2}=0.025

As there is no previous estimate for p

Then, p=0.5

Here on using the table

z(\frac{\alpha }{2}) =1.959963985

Also,

E=0.04

p=0.5

Thus,

n=600.2279407

On approximating the value,

n=601

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muminat

Answer:

V≈184.31

Step-by-step explanation:

V=πr2h

3=π·42·11

3≈184.30677

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3 years ago
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andrew-mc [135]

Answer:

v=\sqrt{\frac{E}{m}}

Step-by-step explanation:

The formula is given as:

E=mv^2

We need to solve this formula for v, that means that v to one side and let it be solved in terms of the other variables (E and m). First, we isolate v:

E=mv^2\\\frac{E}{m}=\frac{mv^2}{m}\\\frac{E}{m}=v^2

To isolate v, and eliminate the "square", we need to take square roots of both sides, that will give us v in terms of the other variables:

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v=\sqrt{\frac{E}{m}}

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3 years ago
A hallway is 9 yards how long is the inches in the hallway
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Refer to the following scenario:You want to see if there is a difference between the exercise habits of Science majors and Math
bekas [8.4K]

Answer:

1. H0: P1 = P2

2. Ha: P1 ≠ P2

3. pooled proportion p = 0.542

4. P-value = 0.0171

5. The null hypothesis failed to be rejected.

At a signficance level of 0.01, there is not enough evidence to support the claim that there is significant difference between the exercise habits of Science majors and Math majors .

6. The 99% confidence interval for the difference between proportions is (-0.012, 0.335).

Step-by-step explanation:

We should perform a hypothesis test on the difference of proportions.

As we want to test if there is significant difference, the hypothesis are:

Null hypothesis: there is no significant difference between the proportions (p1-p2 = 0).

Alternative hypothesis: there is significant difference between the proportions (p1-p2 ≠ 0).

The sample 1 (science), of size n1=135 has a proportion of p1=0.607.

p_1=X_1/n_1=82/135=0.607

The sample 2 (math), of size n2=92 has a proportion of p2=0.446.

p_2=X_2/n_2=41/92=0.446

The difference between proportions is (p1-p2)=0.162.

p_d=p_1-p_2=0.607-0.446=0.162

The pooled proportion, needed to calculate the standard error, is:

p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{82+41}{135+92}=\dfrac{123}{227}=0.542

The estimated standard error of the difference between means is computed using the formula:

s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.542*0.458}{135}+\dfrac{0.542*0.458}{92}}\\\\\\s_{p1-p2}=\sqrt{0.001839+0.002698}=\sqrt{0.004537}=0.067

Then, we can calculate the z-statistic as:

z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.162-0}{0.067}=\dfrac{0.162}{0.067}=2.4014

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

\text{P-value}=2\cdot P(z>2.4014)=0.0171

As the P-value (0.0171) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

At a signficance level of 0.01, there is not enough evidence to support the claim that there is significant difference between the exercise habits of Science majors and Math majors .

We want to calculate the bounds of a 99% confidence interval of the difference between proportions.

For a 99% CI, the critical value for z is z=2.576.

The margin of error is:

MOE=z \cdot s_{p1-p2}=2.576\cdot 0.067=0.1735

Then, the lower and upper bounds of the confidence interval are:

LL=(p_1-p_2)-z\cdot s_{p1-p2} = 0.162-0.1735=-0.012\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= 0.162+0.1735=0.335

The 99% confidence interval for the difference between proportions is (-0.012, 0.335).

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Answer:

Step-by-step explanation:

(-3.1 - 4.92)/2 = -8.02/2 = -4.01

(-2.8 - 3.3)/2 = -6.1/2= -3.05

(-4.01. -3.05) the midpoint

7 0
3 years ago
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