You Explain It! ESP Suppose an acquaintance claims to have the...

Question

You Explain It! ESP Suppose an acquaintance claims to have the ability to determine the birth month of randomly selected individuals. To test such a claim, you randomly select 80 individuals and ask the acquaintance to state the birth month of the individual. If the individual has the ability to determine birth month, then the proportion of correct birth months should exceed 1/12, the rate one would expect from simply guessing.
a. State the null and alternative hypotheses for this experiment.

a. State the null and alternative hypotheses for this experiment.

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A surveyor collects data on 30 randomly selected customers entering a mobile phone store. Each customer is classified as either a first-time visitor F. Or a returning customer are. There are 20 returning customers and 10 first-time visitors. The store manager believes that customers visit randomly by type, meaning there's a 50/50 split between first timers and returners. What is the claim and what are the null and alternative hypotheses for this test? Awesome. So, with that in mind, so we're told that we're trying to determine what is the particular claim for this particular problem. So that's our first answer we're trying to solve for. And our 2nd and 3rd answers are we're trying to determine the null hypothesis, that's our second answer, and the alternative hypothesis, which is our 3rd answer. Awesome. So ultimately for this particular problem, we're trying to solve for three separate answers. So once again we're trying to figure out the claim and the Nolan alternative hypotheses for this particular problem based on the information that is provided to us. So, with that in mind, Our first step is we need to identify the claim, so the store manager claims that the types of customers, first-time visitors versus returning visitors come in equal proportions, meaning 50/50 each. That will mean that the claim, which you'll call C. States that the true proportion of first-time visitors is 0.5 as a decimal, which would mean that it's 50% as a percentage, because you need to take your percent if you want to convert your decimal into a percentage, you just need to take 0.5 multiplied by 100, and when you do, you'll get 50%. So with that in mind, our second step is we need to define the hypotheses, so we need to let P denote the proportion of first-time visitors. Then we can go ahead and write our null hypothesis, which will denote as H0 H subscript 0, and our null hypothesis. States that P is equal to 0.5. And the alternative hypothesis, which we'll call H subscript one or H1, Would therefore as a result be that P cannot equal 0.5. Fantastic. So, Let us quickly recap here. So, once again, our claim is that the true proportion of first-time visitors is 0.5%, which is 50%. When we convert our decimal to a percentage. Our second step is we need to define our hypotheses where we're letting P denote the proportion of first-time visitors. Then we can say we can go ahead and state that our null hypothesis is P is equal to 0.5 because the proportion of first-time visitors is 50%, which would mean that our alternative hypothesis H1 states that P cannot equal 0.5. So that means that the proportion is not 50%, it is either higher or lower, and at this point it's important to note that we need to recall and recognize that this is a two-tail test since we are testing for any difference from 0.5. So that will mean that to recap our final answers, that would mean our final three answers without a doubt, will have to be our claim is proportion is 50%. H0, or null hypothesis is P is equal to 0.5, and our alternative hypothesis H1 is P cannot equal 0.5, and that's it. Those are our final answers. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

Null and Alternative Hypotheses

Proportion in Hypothesis Testing

Random Sampling and Its Importance

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