Question

Matt thinks that he has a special relationship with the number 5. In particular, Matt thinks that he would roll a 5 with a fair 8- sided die more often than you'd expect by chance alone. Suppose p is the true proportion of the time Matt will roll a 5.

(a) State the null and alternative hypotheses for testing Matt's claim. (Type the symbol "p" for the population proportion, whichever symbols you need of "<", "", "not" and express any values as a fraction e.g. p = 1/3)
Hₒ=
Hₐ=

Answer 1

The null hypothesis (H₀) for Matt's claim about the number 5 is that the proportion p is equal to 1/8 (H₀: p = 1/8), indicating a fair die. The alternative hypothesis (Hᴅ) is that the proportion p is greater than 1/8 (Hᴅ: p > 1/8), indicating Matt rolls a 5 more than chance would suggest.

Step-by-step explanation:

When testing Matt's claim about having a special relationship with the number 5 when rolling an 8-sided die, we would set up the null and alternative hypotheses regarding the population proportion p, which represents the true proportion of the time Matt will roll a 5. The test of the hypothesis is based on the assumption that the die is fair, and thus the probability of rolling any single number is equal.

The null hypothesis (H₀) represents the situation under the assumption of no special relationship, meaning that the die is fair and Matt's chances of rolling a 5 are the same as rolling any other number. So, we expect the proportion p to be 1/8, reflecting the fairness of the die:

H₀: p = 1/8

The alternative hypothesis (Hᴅ) represents Matt's claim that he has a special relationship with the number 5 and would roll it more often than chance would allow. Therefore, we're looking for evidence that p is greater than 1/8:

Hᴅ: p > 1/8

The test would involve rolling the die a number of times, recording the occurrences of rolling a 5, and using a statistical test to compare the observed results against what would be expected under the null hypothesis.