A student wants to determine if pennies are really fair, meaning equally likely to land heads up or tails up. He flips a random sample of 50 pennies and finds that 28 of them land heads up. What are the appropriate null and alternative hypotheses? A)H₀: p ≥ 0.5, H_{a :}_{p 0.5} D)H₀: p ≥ 28, H_{a :}_{p

Question

A student wants to determine if pennies are really fair, meaning equally likely to land heads up or tails up. He flips a random sample of 50 pennies and finds that 28 of them land heads up. What are the appropriate null and alternative hypotheses? A)H₀: p ≥ 0.5, H_{a :}_{p < 0.5} B)H₀: p ≤ 0.5, H_{a :}_{p ≠ 0.5} C)H₀: p = 0.5, H_{a :}_{p > 0.5} D)H₀: p ≥ 28, H_{a :}_{p < 28}

Quizplus · Accepted Answer

The appropriate null hypothesis is that the probability of a penny landing heads up is 0.5, and the alternative hypothesis is that the probability is greater than 0.5. This is because we want to test whether pennies are fair (equally likely to land heads up or tails up), and if they are fair, the probability of a penny landing heads up should be 0.5. We do not have enough evidence to support the alternative hypothesis that the probability is less than 0.5, so option A is incorrect. The alternative hypothesis in option B is too vague, and does not specify whether the probability is greater or less than 0.5, so it is also incorrect. Option D is incorrect because the null hypothesis should be a specific value, not based on the sample proportion.

A Student Wants to Determine If Pennies Are Really Fair