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postnew [5]
2 years ago
6

In order for a constitutional amendment to the Florida constitution to pass 60% of the popular vote must support the amendment.

A researcher is interested in determining if the more than sixty percent of the voters would support a new amendment about higher education. The researcher asks 500 random selected potential voters if they would support the amendment. What is the null and alternative hypothesis?
Mathematics
1 answer:
max2010maxim [7]2 years ago
4 0

Answer:

H_{0}: p \leq 0.6\\H_A: p > 0.6

Step-by-step explanation:

We are given the following in the question:

Percentage of vote required for constitutional amendment = 60%

p = 60% = 0.6

Hypothesis:

More than sixty percent of the voters would support a new amendment about higher education.

We design the null and the alternate hypothesis  

H_{0}: p \leq 0.6\\H_A: p > 0.6

Interpretation:

The null hypothesis states that less than or equal to 60% of the voter support the new amendment and the alternative hypothesis states that gretaer than 60% supports the amendment about higher education.

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6.In a sample of 131 women with cosmetic dermatitis from using eye shadow, 12 were diagnosed with a nickel allergy. In a sample
aivan3 [116]

Answer:

a) 0.0916 - 1.96\sqrt{\frac{0.0916(1-0.0916)}{131}}=0.0422

0.0916 + 1.96\sqrt{\frac{0.0916(1-0.0916)}{131}}=0.1410

So then we can conclude that the true proportion of women with cosmetic dermatitis from using eye shadow at 95% of confidence is between (0.0422 and 0.1410)

b) \hat p = \frac{25}{250}= 0.1

0.1 - 1.96\sqrt{\frac{0.1(1-0.1)}{250}}=0.0628

0.1 + 1.96\sqrt{\frac{0.1(1-0.1)}{250}}=0.1372

So then we can conclude that the true proportion of women with cosmetic dermatitis from using mascara at 95% of confidence is between (0.0628 and 0.1372)

c) For this case we see that both confidence intervals contains the value of 0.12 so then we can't conclude that only one group is referenced at the significance level of 0.05 used.

Step-by-step explanation:

Part a

The estimated proportion of women with cosmetic dermatitis from using eye shadow is given by:

\hat p =\frac{12}{131}= 0.0916

The confidence  interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The confidence interval for the proportion is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

Replacing we got:

0.0916 - 1.96\sqrt{\frac{0.0916(1-0.0916)}{131}}=0.0422

0.0916 + 1.96\sqrt{\frac{0.0916(1-0.0916)}{131}}=0.1410

So then we can conclude that the true proportion of women with cosmetic dermatitis from using eye shadow at 95% of confidence is between (0.0422 and 0.1410)

Part b: A 95% confidence interval for the women with cosmetic dermatitis from using mascara

\hat p = \frac{25}{250}= 0.1

0.1 - 1.96\sqrt{\frac{0.1(1-0.1)}{250}}=0.0628

0.1 + 1.96\sqrt{\frac{0.1(1-0.1)}{250}}=0.1372

So then we can conclude that the true proportion of women with cosmetic dermatitis from using mascara at 95% of confidence is between (0.0628 and 0.1372)

Part c: Suppose you are informed that the true proportion with a nickel allergy for one of the two groups (eye shadow or mascara) is .12. Can you determine which group is referenced? Explain.

For this case we see that both confidence intervals contains the value of 0.12 so then we can't conclude that only one group is referenced at the significance level of 0.05 used.

7 0
2 years ago
Trapezoid $RSTU$ is a cross section of a lampshade. The diagonals of $RSTU$ are congruent, and the measure of $\angle S$ is $112
Alexxandr [17]

Answer:

112°

Step-by-step explanation:

Given that the diagonals of trapezoid RSTU are congruent, it is an Isosceles Trapezoid.

One of the properties of an Isosceles Trapezoid is that the base angles are equal.

Therefore if the measure of angle S=112°, the measure of Angle U will also be 112°.

3 0
1 year ago
The solution to that equation is p=500. What does the solution mean?
hjlf

Answer:

that means that the letter p in the equation equals to 500

8 0
2 years ago
In a large population, 61 % of the people have been vaccinated. if 4 people are randomly selected, what is the probability that
muminat
In a large population, 61% of the people are vaccinated, meaning there are 39% who are not. The problem asks for the probability that out of the 4 randomly selected people, at least one of them has been vaccinated. Therefore, we need to add all the possibilities that there could be one, two, three or four randomly selected persons who were vaccinated.

For only one person, we use P(1), same reasoning should hold for other subscripts.

P(1) = (61/100)(39/100)(39/100)(39/100) = 0.03618459
P(2) = (61/100)(61/100)(39/100)(39/100) = 0.05659641
P(3) = (61/100)(61/100)(61/100)(39/100) = 0.08852259
P(4) = (61/100)(61/100)(61/100)(61/100) = 0.13845841

Adding these probabilities, we have 0.319761. Therefore the probability of at least one person has been vaccinated out of 4 persons randomly selected is 0.32 or 32%, rounded off to the nearest hundredths.
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1 year ago
You and a friend are playing a game by tossing two coins. If both coins land
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c. No. You have a probability of winning, while your friend has a
probability of winning.
Or it’s A
3 0
2 years ago
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