A company is marketing a new product they say works better than the traditional test tube. There is so much interest in the product that 30 different labs around the world are testing the claim that this product is actually better. If each study uses an alpha level (alpha) of .10, and if the null hypothesis is true (that the test tube isn't any better that the traditional one), how many of the hypothesis tests would we expect to incorrectly find statistical significance (that is, conclude that the new test tube is better, when it actually isn't)?

Question
Significance tests
asked 2021-01-10
A company is marketing a new product they say works better than the traditional test tube. There is so much interest in the product that 30 different labs around the world are testing the claim that this product is actually better. If each study uses an alpha level (alpha) of .10, and if the null hypothesis is true (that the test tube isn't any better that the traditional one), how many of the hypothesis tests would we expect to incorrectly find statistical significance (that is, conclude that the new test tube is better, when it actually isn't)?

Answers (1)

2021-01-11
Step 1
When a researcher incorrectly rejects the null hypothesis or incorrectly finds the statistical significance, then this type of error is termed as type 1 error. Type 1 error is the rejection of true null hypothesis.
Step 2
The probability of committing a type I error is represented by our alpha level \((\alpha)\), which is the p-value below which we reject the null hypothesis. A p-value of 0.10 indicates that we are willing to accept a 10% chance that we are incorrectly rejecting the null hypothesis.
Hence we expect 10% of the hypothesis tests to incorrectly find statistical significance.
0

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Describe a possible application of hypothesis testing to a business setting. The application you describe need not be a real one (one that has actually occurred), it can be an application that you invent.
You should describe
a) what the business setting is
b) what data you would use
c) what null hypothesis you would test and what the alternative hypothesis is.
d) what type of test you would use
e) You should explain what level of significance you would use and why.
f) You should explain how to interpret the outcome of the test: what does it tell you if you could reject or could not reject the null hypothesis?
g) Finally, you should explain the possible advantages of using hypothesis testing in this application and its possible downsides / dangers (when / how using a hypothesis test could lead to mistaken inferences or erroneous decisions).
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