Mixing
Finding Alpha Level from Rejection Rule
$begingroup$
I have a question which asks:
A researcher wants to evaluate the sensitivity of their assay for
measuring urinary mercury. The standard is to have a 99% probability
of detecting a sample with mercury concentration 1 ppm. Therefore,
they wish to test the null hypothesis H_0: p=0.99, where p is the
probability of a positive test when the concentration is 1 ppm. The
alternative hypothesis is that p is not equal to 0.99. The researcher
created 500 samples with a 1ppm mercury concentration and tested them.
The number of samples that tested positive was recorded.
2.1. Suppose that they decide to reject H_0 if the number of positive samples is 494 or less. What is the type I error probability of this
rejection rule?
If the null hypothesis is true, we expect 99% of the samples to be positive, which is 495 samples. So this rejection rule says that if anything less than 99% are positive we are rejecting the null. This seems like it must be a high alpha (a high probability of rejecting a true null hypothesis due to chance), but I'm confused about how to calculate it.
statistics hypothesis-testing
asked Jan 23 at 19:41
hemerahemera
11
$endgroup$
add a comment |
$begingroup$
I have a question which asks:
A researcher wants to evaluate the sensitivity of their assay for
measuring urinary mercury. The standard is to have a 99% probability
of detecting a sample with mercury concentration 1 ppm. Therefore,
they wish to test the null hypothesis H_0: p=0.99, where p is the
probability of a positive test when the concentration is 1 ppm. The
alternative hypothesis is that p is not equal to 0.99. The researcher
created 500 samples with a 1ppm mercury concentration and tested them.
The number of samples that tested positive was recorded.
2.1. Suppose that they decide to reject H_0 if the number of positive samples is 494 or less. What is the type I error probability of this
rejection rule?
If the null hypothesis is true, we expect 99% of the samples to be positive, which is 495 samples. So this rejection rule says that if anything less than 99% are positive we are rejecting the null. This seems like it must be a high alpha (a high probability of rejecting a true null hypothesis due to chance), but I'm confused about how to calculate it.
statistics hypothesis-testing
asked Jan 23 at 19:41
hemerahemera
11
$endgroup$
add a comment |
$begingroup$
I have a question which asks:
A researcher wants to evaluate the sensitivity of their assay for
measuring urinary mercury. The standard is to have a 99% probability
of detecting a sample with mercury concentration 1 ppm. Therefore,
they wish to test the null hypothesis H_0: p=0.99, where p is the
probability of a positive test when the concentration is 1 ppm. The
alternative hypothesis is that p is not equal to 0.99. The researcher
created 500 samples with a 1ppm mercury concentration and tested them.
The number of samples that tested positive was recorded.
2.1. Suppose that they decide to reject H_0 if the number of positive samples is 494 or less. What is the type I error probability of this
rejection rule?
If the null hypothesis is true, we expect 99% of the samples to be positive, which is 495 samples. So this rejection rule says that if anything less than 99% are positive we are rejecting the null. This seems like it must be a high alpha (a high probability of rejecting a true null hypothesis due to chance), but I'm confused about how to calculate it.
statistics hypothesis-testing
asked Jan 23 at 19:41
hemerahemera
11
$endgroup$
I have a question which asks:
A researcher wants to evaluate the sensitivity of their assay for
measuring urinary mercury. The standard is to have a 99% probability
of detecting a sample with mercury concentration 1 ppm. Therefore,
they wish to test the null hypothesis H_0: p=0.99, where p is the
probability of a positive test when the concentration is 1 ppm. The
alternative hypothesis is that p is not equal to 0.99. The researcher
created 500 samples with a 1ppm mercury concentration and tested them.
The number of samples that tested positive was recorded.
2.1. Suppose that they decide to reject H_0 if the number of positive samples is 494 or less. What is the type I error probability of this
rejection rule?
If the null hypothesis is true, we expect 99% of the samples to be positive, which is 495 samples. So this rejection rule says that if anything less than 99% are positive we are rejecting the null. This seems like it must be a high alpha (a high probability of rejecting a true null hypothesis due to chance), but I'm confused about how to calculate it.
statistics hypothesis-testing
statistics hypothesis-testing
asked Jan 23 at 19:41
hemerahemera
11
asked Jan 23 at 19:41
hemerahemera
11
asked Jan 23 at 19:41
hemerahemera
11
asked Jan 23 at 19:41
hemerahemera
11
asked Jan 23 at 19:41
hemerahemera
11
11
add a comment |
add a comment |
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