Mathematics: I need to find the proportion for this problem

I need to find the proportion for this problem, №9519338, 10.04.2022 05:50

English

A pollster is interested in comparing the proportions of women and men in a particular town who are in favor of a ban on fireworks within town borders. The pollster plans to test the hypothesis that the proportion of women in favor of the ban is diﬀerent from the proportion of men in favor of the ban. There are 4,673 women and 4,502 men who live in the town. From a simple random sample of 40 women in the town, the pollster finds that 38 favor the ban. From an independent simple random sample of 50 men in the town, the pollster finds that 27 favor

Step-by-step answer

P Answered by PhD

3

A two-proportion z-test would not be valid for these data.

Option E.

Explanation:

Z test is a type of a statistical test for which the distribution of the data, the distribution of the test statistic under the null hypothesis is made with the help of the and under the normal distribution.

The purpose and the aim of the Z test is to test mean of the distribution of the data but the condition of applying a Z test in the sample is that the variance of the population should be known. Without knowing the variance of the population, we can not apply it.

English

A pollster is interested in comparing the proportions of women and men in a particular town who are in favor of a ban on fireworks within town borders. The pollster plans to test the hypothesis that the proportion of women in favor of the ban is diﬀerent from the proportion of men in favor of the ban. There are 4,673 women and 4,502 men who live in the town. From a simple random sample of 40 women in the town, the pollster finds that 38 favor the ban. From an independent simple random sample of 50 men in the town, the pollster finds that 27 favor

Step-by-step answer

P Answered by PhD

3

A two-proportion z-test would not be valid for these data.

Option E.

Explanation:

Z test is a type of a statistical test for which the distribution of the data, the distribution of the test statistic under the null hypothesis is made with the help of the and under the normal distribution.

The purpose and the aim of the Z test is to test mean of the distribution of the data but the condition of applying a Z test in the sample is that the variance of the population should be known. Without knowing the variance of the population, we can not apply it.

Mathematics

According to a recent census, 14.6% of all housing units in a certain country are vacant. A county supervisor wonders if her county is different from this. She randomly selects 865 housing units in her county and finds that 159 of the housing units are vacant. Name the model and check appropriate conditions for a hypothesis test. What kind of test is this? A. One-proportion z-test B. Two-proportion t-test C. Proportional t-test D. Difference in proportions test

Step-by-step answer

P Answered by PhD

We need to conduct a hypothesis in order to test the claim that the true proportion is equal to 14.6% or not. So we need to use a one proportion z test and the system of hypothesis are:

Null hypothesis: p=0.146

Alternative hypothesis: $p \neq 0.146$

A. One-proportion z-test

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

And the conditions required are:

1) The data comes from a random sampling

2) Independence condition between observations

3) np>10 and n(1-p)>10

4) The sample size is 10 times lower than the population size.

Step-by-step explanation:

Data given and notation

n=865 represent the random sample taken

X=159 represent the housing units that are vacant

$\hat p=\frac{159}{865}=0.184$ estimated proportion of vacant units

p_o=0.146 is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)

Solution to the problem

We need to conduct a hypothesis in order to test the claim that the true proportion is equal to 14.6% or not. So we need to use a one proportion z test and the system of hypothesis are:

Null hypothesis: p=0.146

Alternative hypothesis: $p \neq 0.146$

A. One-proportion z-test

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

And the conditions required are:

1) The data comes from a random sampling

2) Independence condition between observations

3) np>10 and n(1-p)>10

4) The sample size is 10 times lower than the population size.

Mathematics

According to a recent census, 14.6% of all housing units in a certain country are vacant. A county supervisor wonders if her county is different from this. She randomly selects 865 housing units in her county and finds that 159 of the housing units are vacant. Name the model and check appropriate conditions for a hypothesis test. What kind of test is this? A. One-proportion z-test B. Two-proportion t-test C. Proportional t-test D. Difference in proportions test

Step-by-step answer

P Answered by PhD

We need to conduct a hypothesis in order to test the claim that the true proportion is equal to 14.6% or not. So we need to use a one proportion z test and the system of hypothesis are:

Null hypothesis: p=0.146

Alternative hypothesis: $p \neq 0.146$

A. One-proportion z-test

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

And the conditions required are:

1) The data comes from a random sampling

2) Independence condition between observations

3) np>10 and n(1-p)>10

4) The sample size is 10 times lower than the population size.

Step-by-step explanation:

Data given and notation

n=865 represent the random sample taken

X=159 represent the housing units that are vacant

$\hat p=\frac{159}{865}=0.184$ estimated proportion of vacant units

p_o=0.146 is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)

Solution to the problem

We need to conduct a hypothesis in order to test the claim that the true proportion is equal to 14.6% or not. So we need to use a one proportion z test and the system of hypothesis are:

Null hypothesis: p=0.146

Alternative hypothesis: $p \neq 0.146$

A. One-proportion z-test

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

And the conditions required are:

1) The data comes from a random sampling

2) Independence condition between observations

3) np>10 and n(1-p)>10

4) The sample size is 10 times lower than the population size.

Mathematics

You want to know if there s a difference between the proportions of high-school students and college students who read newspapers regularly. out of a random sample of 500 high-school students, 287 say they read newspapers regularly, and out of a random sample of 420 college students, 252 say they read newspapers regularly. for this question, think of high-school students as sample one and college students as sample two. a. construct a 95% confidence interval for the difference between the proportions of high-school students and college students

Step-by-step answer

P Answered by Specialist

3

The proportion of high-school students who read the newspaper on a regular basis is not less than the proportion of college students who read newspapers regularly

Step-by-step explanation:

Sample High school college total

N 500 420 920

X 287 252 539

p 0.574 0.6 0.586

A) Sample size is very large and also proportions are nearer to 0.5 hence binomial approximates to normal so Z can be used.

Var (p1-p2) = Var(p1)+Var(p2)

Std def for difference = $\sqrt{p(1-p)(\frac{1}{n_1} +\frac{1}{n_2})} \\=\sqrt{0.586(1-0.586)(\frac{1}{500} +\frac{1}{420})\\=0.0326$

Margin of error =1.96* std error = 0.0639

Confidence interval = p difference ±margin of error

= (-0.0899, -0.0639)

B) Since 95% confidence interval contains 0, there is no significant difference between the two proportions

C) H0: p1 = p2

Ha: p1 <p2

D) Pooled estimate = 0.586

E) Yes because sample sizes are large and proportion is nearer to 0.5

G) Z = -0.7975

p value = 0.21186(one tailed)

H) Since p value is greater than 0.05 our significant level, we accept null hypothesis.

The proportion of high-school students who read the newspaper on a regular basis is not less than the proportion of college students who read newspapers regularly

Mathematics

Several factors are involved in the creation of a confidence interval. Among them are the sample size, the level of confidence, and the margin of error. Which statements are true? 1) For a given sample size, lower confidence means a smaller margin of error. Is the statement true? A) The statement is true. A larger margin of error creates a wider confidence interval, which is more likely to contain the population parameter. B) The statement is true. A larger margin of error creates a more narrow confidence interval, which is less likely to contain

Step-by-step answer

P Answered by Specialist

AACB

Step-by-step explanation:

1) The statement is true. A larger margin of error creates a wider confidence interval, which is more likely to contain the population parameter.

2) The statement is false. A larger sample size decreases the standard error of the sample proportion, which decreases the margin of error.

3) The statement is true. A smaller sample size increases the standard error of the sample proportion, which, for a fixed margin of error, decreases the critical value, z*.

4) The statement is true. One can see from the margin of error formula that the margin of error is inversely proportional to the square root of n.

Mathematics

Independent random samples of students were taken from two high schools, R and S, and the proportion of students who drive to school in each sample was recorded. The difference between the two sample proportions (R minus S) was 0.07. Under the assumption that all conditions for inference were met, a hypothesis test was conducted where the alternative hypothesis was the population proportion of students who drive to school for R was greater than that for S. The p-value of the test was 0.114. Which of the following is the correct interpretation of

Step-by-step answer

P Answered by PhD

5

Correct option: (D).

Step-by-step explanation:

The hypothesis for testing whether there is a difference between the two population proportions is:

H₀: The population proportion of students who drive to school for R and S is same, i.e. p₁ = p₂.

Hₐ: The population proportion of students who drive to school for R was greater than that for S, i.e. p₁ > p₂.

The difference between the two sample proportion is,

$\hat p_{1}-\hat p_{2}=0.07$

And the p-value of the test is:

p-value = 0.114

The p-value is well defined as the probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or greater than what was the truly observed value of the test statistic.

We reject a hypothesis if the p-value of a statistic is lower than the level of significance α.

The p-value of 0.114 indicates that, assuming the null hypothesis to be true, the probability of obtaining a difference between the two sample proportions of at least 0.07 is 0.114.

The correct option is (D).

Mathematics

Studies indicate that about 10 percent of polar bears weigh more than 1,000 pounds. A biologist studying the bears thinks that percent might be too high. From a random sample of polar bears, the biologist found only 8 percent of the sample weighing over 1,000 pounds. Which of the following is the most appropriate method for the biologist’s study? A one-sample z -test for a sample proportion A one-sample z -test for a sample proportion A one-sample z -test for a population proportion A one-sample z -test for a population proportion A one-sample

Step-by-step answer

P Answered by PhD

B) A one sample Z test for a population proportion

Step-by-step explanation: Trust me bro.

Mathematics

Independent random samples of students were taken from two high schools, R and S, and the proportion of students who drive to school in each sample was recorded. The difference between the two sample proportions (R minus S) was 0.07. Under the assumption that all conditions for inference were met, a hypothesis test was conducted where the alternative hypothesis was the population proportion of students who drive to school for R was greater than that for S. The p-value of the test was 0.114. Which of the following is the correct interpretation of

Step-by-step answer

P Answered by PhD

5

Correct option: (D).

Step-by-step explanation:

The hypothesis for testing whether there is a difference between the two population proportions is:

H₀: The population proportion of students who drive to school for R and S is same, i.e. p₁ = p₂.

Hₐ: The population proportion of students who drive to school for R was greater than that for S, i.e. p₁ > p₂.

The difference between the two sample proportion is,

$\hat p_{1}-\hat p_{2}=0.07$

And the p-value of the test is:

p-value = 0.114

The p-value is well defined as the probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or greater than what was the truly observed value of the test statistic.

We reject a hypothesis if the p-value of a statistic is lower than the level of significance α.

The p-value of 0.114 indicates that, assuming the null hypothesis to be true, the probability of obtaining a difference between the two sample proportions of at least 0.07 is 0.114.

The correct option is (D).

Mathematics

After 6 months, the total cost of tanya’s gym membership was $200. after 8 months, the total cost was $260. is this a proportional or non-proportional relationship? question 11 options: proportional; the constant of proportionality is $33.33/month proportional; the constant of proportionality is $32.50/month non-proportional; the rate of change is $20/month non-proportional; the rate of change is $30/month

Step-by-step answer

P Answered by PhD

3

Non-proportional; the rate of change is $30/month

Step-by-step explanation:

After 6 months, the total cost was $200.

After 8 months, the total cost was $260.

Find the rate of change using formula

$\dfrac{f(b)-f(a)}{b-a}$

Hence,

$\text{Rate of change}\\ \\=\dfrac{\$260-\$200}{8-6}\\ \\=\dfrac{\$60}{2}\\ \\=\$30\ \text{per month}$

At this rate, after 6 months Tanya paid

$\$30\cdot 6=\$180$

But after 6 months, the total cost of Tanya’s gym membership was $200.

It means the relationship passes through the point (0,20), not through the origin. Each proportional realtionship passes through the origin. Thus, this is not proportional relationship.

I need to find the proportion for this problem

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