A manufacturer claims that 20% of sugar-coated chocolate beans are red. George suspects that this percentage is actually less than 20% and so he takes a random sample of 15 chocolate beans and performs a hypothesis test with the null hypothesis $p = 0.2$ against the alternative hypothesis $p < 0.2$. He decides to reject the null hypothesis in favour of the alternative hypothesis if there are 0 or 1 red beans in the sample. (i) With reference to this situation, explain what is meant by a Type I error. (ii) Find the probability of a Type I error in George's test.
Added by John S.
Close
Step 1
A Type I error occurs when the null hypothesis is true, but we incorrectly reject it. In this problem: The null hypothesis ($H_0$) is that the proportion of red chocolate beans is $p = 0.2$. The alternative hypothesis ($H_1$) is that the proportion of red Show more…
Show all steps
Your feedback will help us improve your experience
Qudsiya Anis and 61 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
1 - Hypothesis Testing LEARNING OBJECTIVE: Determine the null and alternative hypotheses in a given situation. Jackson wants to test an assumption on the number of red candies in a bag of Fruity Tooty's candy. The company claims that five flavors are given an equal distribution in each bag, meaning that the proportion of each color should be 20%. Jackson decides to focus his efforts on examining whether there is a difference in the proportion of red candies than what the company claims. What should Jackson state for the null hypothesis and alternative hypothesis? a.) Null hypothesis: p = 0.20 Alternative hypothesis: p = 0.20 b.) Null hypothesis: p = 0.20 Alternative hypothesis: p > 0.20 c.) Null hypothesis: p = 0.20 Alternative hypothesis: p < 0.20 d.) Null hypothesis: p > 0.20 Alternative hypothesis: p < 0.20
Qudsiya A.
James was eating a bag of candies that came in eight different colors. He noticed that there appeared to be far fewer green candies than any of the others and wondered if the true proportion of green candies is lower than the 12.5% that would be expected if all of the candies came in even amounts. For the sake of statistics, he decided that he would need to buy more candy to test his hypothesis. James randomly selected several bags of candies and recorded the color of each piece of candy. He found that out of the first 400 candies that he counted, 37 of them were green. James conducts a one-proportion hypothesis test at the 5% significance level to test whether the true proportion of green candies was lower than 12.5%. (a) Which answer choice shows the correct null and alternative hypotheses for this test? Select the correct answer below: H0: p = 0.125; Ha: p < 0.125, which is a left-tailed test.
Sri K.
(1) How one calculates the level of significance: Assume that in flipping an ordinary coin, the probabilities of heads and tails are both 50%. Suppose that Mr. G, a coin collector, has a rare dime whose probabilities of heads and tails are 60% and 40% respectively. Imagine that for some reason Mr. G misplaces his rare dime. Later he finds a dime that is identical in appearance and wonders if it is his rare dime. To help him make a decision, he sets up a test of hypotheses: Ha: p = 60% and H0: p = 50%. Let us assume that Mr. G flips the coin 10 times. Furthermore, suppose he decided that if the 10 flips yield 6 or more heads, he will assume that the coin he found is his rare dime, whereas if the 10 flips yield fewer than 6 heads, he will assume that the coin he found is an ordinary coin. Calculate ̑ = P(making a type I error) = P(test will reject H0 when Ha is true). We can use the binomial distribution here. Trust that instinct: (If your statistically savvy side is saying "error means in the context of the problem," start this problem by writing what making the Type I error means and note that ̑ is actually a conditional probability!)
Adi S.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD