Hypothesis Testing  Practice Problems

1. With a perfectly balanced roulette wheel, in the long run red numbers should turn up 18 times in 38.  A gambler suspects that a particular roulette wheel produces too few Reds.  To test this, he notes that out of 6000 plays, 2806 come up Red.  Is that too few?  Or chance variations?
    a) State the null and alternative hypothesis as statements about a box model.
    b) What is the value of the test statistic z?
    c) What is the p-value?
    d) Were there too few Reds?
 

2. To test psychic abilities, parapsychologists use a special deck of cards that have five symbols that are simple and yet look fairly different from each other.  (For example, squiggly lines, circle, star, etc.)  The deck has 100 cards, and there are 20 of each symbol.  To test whether someone can read minds, a "target" randomly selects a card from the deck, looks at the card, and concentrates on that symbol.  In another room, the possible psychic then indicates which symbol he or she thinks the target has selected.  The investigator records whether the psychic was right or wrong.  The card is returned to the deck, shuffled, and everything begins again.   Suppose that, in 150 tries, a possible psychic gets 32 right.  Is this evidence of psychic ability, or is it more easily explained by chance variation?
    a) State the null and alternative hypotheses as statements about a box model.
    b) What is the value of the test statistic z?
    c) What is the p-value?
    d) What do you conclude?
 

Click here for solutions!