Power of Test of the hypothesis

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Thomas74

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Hello,

I'm working on my homework, if you have free time, please kindly check my work.

Thank you,

Here's the problem:
1. We asked at the poll 400 voters if they voted for party A. 168 of them responded that they did. Estimate the absolute number of voters of this party assuming, that there are 8 000 voters. Use 95 % confidence level and continuity correction. (I'm done with this part). Assume the null hypothesis to be that the party has 50 % or more voters and the minimal effect size of interest is 10 percentage points. What is the power of the test assuming minimal effect size? What is the decision of the test? (I don't know how to do this one).


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2. Accuracy of a coffee vending machine is given by standard deviation equal to 10 ml. A new vending machine was bought. Test the hypothesis, that the new vending machine is less accurate (s.d. is larger) than was the old one, if we measured among 15 randomly chosen cups of coffee sample´s variance 150.8. What is the power of the test if the true new standard deviation is, consequently, 12, 14 or 16 ml? (My work has been posted below, please kindly check it)

Thank you, freemathhelp!
 

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Thomas74 said:
Hello,

I'm working on my homework, if you have free time, please kindly check my work.

Thank you,

Here's the problem:
1. We asked at the poll 400 voters if they voted for party A. 168 of them responded that they did. Estimate the absolute number of voters of this party assuming, that there are 8 000 voters. Use 95 % confidence level and continuity correction. (I'm done with this part). Assume the null hypothesis to be that the party has 50 % or more voters and the minimal effect size of interest is 10 percentage points. What is the power of the test assuming minimal effect size? What is the decision of the test? (I don't know how to do this one).


View attachment 30289




2. Accuracy of a coffee vending machine is given by standard deviation equal to 10 ml. A new vending machine was bought. Test the hypothesis, that the new vending machine is less accurate (s.d. is larger) than was the old one, if we measured among 15 randomly chosen cups of coffee sample´s variance 150.8. What is the power of the test if the true new standard deviation is, consequently, 12, 14 or 16 ml? (My work has been posted below, please kindly check it)

Thank you, freemathhelp!
Click to expand...
It's been a while since I do hypothesis testing. Will take me some time to refresh, but I can give you a few things I noticed so far.
Q1)
  1. Second, what you've done is calculate the confidence interval of voters who will vote for party A. The question is asking for an absolute estimate of # of voters. I'm not sure this means the same thing?
  2. There's a typo error in the last line where it's cut off. Your lower value is .37 but you wrote .31 instead.
Q2) I think the question is missing the significance level. Anyways, you calculated the chi-squared stat, now what's your degree of freedom? Then look up the p-value from the chi-square distribution table.
Under what condition do we reject/accept the null? Keep in mind this is a one-tail test. Then make your conclusion.
 
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BigBeachBananas said:
It's been a while since I do hypothesis testing. Will take me some time to refresh, but I can give you a few things I noticed so far.
Q1)
  1. Second, what you've done is calculate the confidence interval of voters who will vote for party A. The question is asking for an absolute estimate of # of voters. I'm not sure this means the same thing?
  2. There's a typo error in the last line where it's cut off. Your lower value is .37 but you wrote .31 instead.
Q2) I think the question is missing the significance level. Anyways, you calculated the chi-squared stat, now what's your degree of freedom? Then look up the p-value from the chi-square distribution table.
Under what condition do we reject/accept the null? Keep in mind this is a one-tail test. Then make your conclusion.
Click to expand...
"It's been a while since I do hypothesis testing. Will take me some time to refresh" thank you @BigBeachBananas :)
I think I already did continuity correction, I highlighted it with red color.
for no.1 I don't know how to calculate the power of test, with this interval and given values.;)
for no.2 same thing happened, I don't know how to calculate the power of test, with the new standard deviation.

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Is there any material on the power of the test of hypothesis in your textbook/lecture material? I find the null hypothesis to be odd. "Assume the null hypothesis to be that the party has 50 % or more". It will translate to something like [math]H_o:\mu\ge.42(1.5)\\ H_1:\mu<.42(1.5)\\[/math]
 
BigBeachBananas said:
Is there any material on the power of the test of hypothesis in your textbook/lecture material? I find the null hypothesis to be odd. "Assume the null hypothesis to be that the party has 50 % or more". It will translate to something like [math]H_o:\mu\ge.42(1.5)\\ H_1:\mu<.42(1.5)\\[/math[ATTACH type="full"]30296[/ATTACH][/math]
Click to expand...
[/QUOTE]


I've searched the formula in my textbook and lecture material but there's none of it. The one that looks similar to it, is only this, but I don't even know how to apply it to my homework. I don't know how to calculate power of the test if P-value is known.
 

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I think I would be able to help you with q2. I would like to know your extensive understanding of the power of tests. So I don't have to go too much in-depth. If you already have a basic knowledge of what it is.
 
I don't know much about the Power of test, I just know that power or beta is the probability to decline null hypothesis if the alternative hypothesis was wrong.
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Example 2 is pretty similar to your question 1.
Example 1 is pretty similar to your question 2, except you're comparing variances instead of mean. So you need to compute the chi-squared critical value, instead of the z-value.
 
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