Why is surface area measured in square units?
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Answer:
The claim that needs to be tested is that the proportion of people who prefer mechanical methods of water sanitizing truly exceeds the proportion of people who have no sanitizing methods preferences. This can be expressed as the population proportion of people who prefer mechanical methods of water sanitizing is significantly higher than 0.5.
This is a hypothesis test for a population proportion.
The test will have null and alternative hypothesis:
Test statistic z = 0.972
P-value = 0.166
At a significance level of 0.05, there is not enough evidence to support the claim that the proportion of people who prefer mechanical methods of water sanitizing truly exceeds the proportion of people who have no sanitizing methods preferences.
Step-by-step explanation:
We have to construct a hypothesis test for the population proportion. We need to test the claim that the proportion of people who prefer mechanical methods of water sanitizing truly exceeds the proportion of people who have no sanitizing methods preferences.
As the survey is done as a yes/no question, the null hypothesis would state that the amount of people who prefer mechanical methods of water sanitizing is not significantly different from the proportion of people who have no sanitizing methods preferences. That can be expressed as the population proportion equals 0.5, so both proportions are equal.
The alternative hypothesis would state that the proportion of people who prefer mechanical methods of water sanitizing truly exceeds the proportion of people who have no sanitizing methods preferences. This could be expressed as the population proportion significantly bigger than 0.5.
Then, the null and alternative hypothesis are written:
The significance level is assumed to be 0.05.
The sample has a size n=209.
The sample proportion is p=0.536.
The standard error of the proportion is:
Then, we can calculate the z-statistic as:
This test is a right-tailed test, so the P-value for this test is calculated as:
As the P-value (0.166) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the proportion of people who prefer mechanical methods of water sanitizing truly exceeds the proportion of people who have no sanitizing methods preferences.
Hey there! Hello!
So, to set this problem up, all you need to do is imagine that the smallest number of these consecutive integers is x. The next two numbers will be x+1, then x+2, and that, altogether, will equal 87. In a problem, this will look like this:
All we need to do is solve for x! We can simplify the problem by combining like terms:
Now that we know what x is, we can plug it into our original problem:
Hope this helped you out! Feel free to ask me any additional questions if you need further clarification. :-)
So, to set this problem up, all you need to do is imagine that the smallest number of these consecutive integers is x. The next two numbers will be x+1, then x+2, and that, altogether, will equal 87. In a problem, this will look like this:
All we need to do is solve for x! We can simplify the problem by combining like terms:
Now that we know what x is, we can plug it into our original problem:
Hope this helped you out! Feel free to ask me any additional questions if you need further clarification. :-)