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# Statistics: Is the Earth Getting Warmer?

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A certain researcher thinks that the proportion of women say that the earth is getting warmer is greater than the proportion of men.
In a random sample of 250 women, 70% said that the earth is getting warmer.
In a random sample of 220 men, 68.18% said that the earth is getting warmer.

At the .05 significance level, is there sufficient evidence to support the claim that the proportion of women saying the earth is getting warmer is higher than the proportion of men saying the earth is getting warmer?

What is the Null Hypothesis?

What is the Alternate Hypothesis?

Calculate the pooled probability of success.

What is the numerical value of Z critical?

What is the numerical value of the test statistic?

What is the P- value for the this Hypothesis test?

What is your decision based upon this Hypothesis test?

https://brainmass.com/statistics/descriptive-statistics/statistics-is-the-earth-getting-warmer-547788

#### Solution Preview

Let P1 is the proportion of all women saying the earth is getting warmer and P2 be the proportion of all men saying the earth is getting warmer

What is the Null Hypothesis?
Ans: Ho: P1=P2

What is the Alternate Hypothesis?
Ans: Ha: P1>P2

Calculate the ...

#### Solution Summary

The solution gived detailed steps on performing a hypothesis testing on two population proportions. All formula and calcuations are shown and explained.

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## Comprehension of Statistics

1. Given a sample size of 65, with sample mean 726.2 and sample standard deviation 85.3, we perform the following hypothesis test.
H0: μ= 750
H1: μ< 750
What is the conclusion of the test at the level? Explain your answer 0.10α=

2. Consider the hypothesis test given by :
H0: μ = 530
H1: μ=≠ 530
In a random sample of 81 subjects, the sample mean is found to be X=524. Also, the population standard deviation is σ= 27
Determine the P-value for this test. Is there sufficient evidence to justify the rejection of H 0 at the α = 0.01 level? Explain

3. A certain researcher thinks that the proportion of women who say that the earth is getting warmer is greater than the proportion of men.
In a random sample of 250 women, 70% said that the earth is getting warmer.
In a random sample of 220 men, 68% said that the earth is getting warmer.
At the 0.05 significance level, is there sufficient evidence to support the claim that the proportion of women saying the earth is getting warmer is higher than the proportion of men saying the earth is getting warmer? Show all work and justify your answer.

Refer to the following data for Questions 4 and 5.
x 0 -1 1 2 3
y 2 -2 5 4 7

4. Is there a linear correlation between x and y at the 0.05 significance level? Justify your answer.

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Color Brown Yellow Orange Green Tan
Number 45 13 17 7 18
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