Spinning a coin, unlike tossing it, may not give heads and tails equal probabilities. I spun a penny 150 times and got 65 heads. We wish to find how significant is this evidence against equal probabilities.

a. What is the sample proportion of heads? Round to 3 places.

b. Heads do not make up half of the sample. Is this sample evidence that the probabilities of heads and tails are different?

Take p to be the probability of getting heads in a spin of a penny. Which hypotheses do we want to test?

• H₀: p ≠ 0.5
• H₀: p = 0.5
• H₀: p = 0.5
• H₀: p > 0.5
• H₀: p = 0.5
• H₀: p ≠ 0.5
• H₀: p = 0.5
• H₀: p < 0.5

c. Compute the z test statistic.

z = 

 Round to 2 places.