Felix purchased a trick coin that is supposed to land heads up 75% of the time. One of his friends volunteers to test this claim. The friend flips the coin 50 times and finds that the coin lands heads up 35 times. The friend then performs a test of the following hypotheses at the alpha = 0.10 significance level:
Ho: p = 0.75
Ha: p < 0.75
where p = the true proportion of tosses of this coin that would land heads-up.
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Question 1
1.
Describe a Type I error in this setting.
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Question 2
2.
Describe a Type II error in this setting.
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Question 3
3.
Which type of error may result in Felix returning the coin and writing a negative review of the product?
Question 4
4.
If the student were to use alpha = 0.05 instead of alpha = 0.10, would this make it more or less likely to reject the null hypothesis when the null hypothesis is true? Explain.