Question

Spinning a coin, unlike tossing it, may not give heads and tails in equal proportions. I spin a penny 125 times and get 54 heads. We want to know if we have significant evidence that the coin lands on heads at a proportion that is different than 50% of the time in the long run.

(a) When we go to the One Proportion applet, what value should be entered under "Probability of heads" (or "Probability of success π ")? Round to 3 places. (b) In the applet, what value should be entered under "Number of tosses" (or "Sample size (n)")?
(c) The simulated distribution of sample statistics will be centered at approximately what value when we click on "Proportion of successes"?
(d) The simulated distribution of sample statistics will be centered at approximately what value when we click on "Number of successes"?

Answer 1

To determine if the coin lands on heads at a proportion that is different than 50% of the time in the long run, we can use the One Proportion applet. In the applet, we need to enter the values of the proportion of heads obtained in the experiment and the total number of spins. The simulated distribution of sample statistics will be centered at the proportion of heads (0.432) and the number of heads (54).

Step-by-step explanation:

To determine if the coin lands on heads at a proportion that is different than 50% of the time in the long run, we can use the One Proportion applet. In the applet, we need to enter the following values:

(a) Under 'Probability of heads' or 'Probability of success π', we should enter the value of the proportion of heads obtained in the experiment. In this case, it would be 54/125, which is approximately 0.432.

(b) Under 'Number of tosses' or 'Sample size (n)', we should enter the total number of times the coin was spun, which is 125.

(c) When we click on 'Proportion of successes', we will find that the simulated distribution of sample statistics will be centered at approximately 0.432.

(d) When we click on 'Number of successes', we will find that the simulated distribution of sample statistics will be centered at approximately 54.