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Chapter 8: Problem 95

A friend claims he can predict the suit of a card drawn from a standard deck of 52 cards. There are four suits and equal numbers of cards in each suit. The parameter, \(p\), is the probability of success, and the null hypothesis is that the friend is just guessing. a. Which is the correct null hypothesis? i. \(p=1 / 4\) ii. \(p=1 / 13\) iii. \(p>1 / 4\) iv. \(p>1 / 13\) b. Which hypothesis best fits the friend's claim? (This is the alternative hypothesis.) i. \(p=1 / 4\) ii. \(p=1 / 13\) iii. \(p>1 / 4\) iv. \(p>1 / 13\)

Short Answer

Expert verified
The correct null hypothesis is \( p=1/4 \) and the hypothesis that best fits the friend's claim (i.e., the alternative hypothesis) is \( p > 1/4 \).

Step by step solution

01

Identify the Null Hypothesis

The null hypothesis is the assumption that the friend's prediction is merely by chance, i.e. he is just guessing. As there are 4 suits of cards, each card drawn randomly has a 1 in 4 or \( p = 1/4 \) chance of belonging to a specific suit. Therefore, looking at our options, the correct null hypothesis is \( p=1/4 \). This describes the probability of success (predicting the right suit) if the friend is just guessing.
02

Identify the Alternative Hypothesis

The alternative hypothesis corresponds to the friend's claim that he can predict the suit of the card. It should represent greater success than mere guessing. Hence, success would be something greater than \( p=1/4 \), implying that the friend is correct more often than just random guessing would predict. Therefore, the alternative hypothesis best fitting the friend's claim is \( p > 1/4 \).

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Most popular questions from this chapter

Suppose you are testing someone to see whether he or she can tell butter from margarine when it is spread on toast. You use many bite-sized pieces selected randomly, half from buttered toast and half from toast with margarine. The taster is blindfolded. The null hypothesis is that the taster is just guessing and should get about half right. When you reject the null hypothesis when it is actually true, that is often called the first kind of error. The second kind of error is when the null is false and you fail to reject. Report the first kind of error and the second kind of error.

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