V At a magic shop, the salesperson shows you a coin that he says will land on heads more than 74% of the times it is flipped. In an attempt to convince you he's correct, the salesperson asks you to try the coin yourself. You flip the coin 65 times. (Consider this a random sample of coin flips.) The coin lands on heads $3 of those times. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to support the salesperson's claim that the proportion, p, of all times the coin lands on heads is more than 74%. () State the null hypothesis Ho and the alternative hypothesis #, that you would use for the test. H: 020 0-0 0-0 X 5 (b) For your hypothesis test, you will use a Z-test. Find the values of ap and s (1-p) to confirm that a Z-test can be used. (One standard is that ap 2 10 and a (1 -p) 2 10 under the assumption that the null hypothesis is true.) Here , is the sample size and p is the population proportion you are testing. 5 ? = (1-P)=0 (c) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. The value of the test statistic is given by PP P(L- P) The p-value is the area under the curve to the right of the value of the test statistic. Standard Normal Distribution Step 1: Select one-tailed or two-tailed. o One-tailed O Two-talled Step 2: Enter the test statistic. (Round to 3 decimal places.) Step 3: Shade the area represented by the p- X ? Step 2: Enter the test statistic. (Round to 3 decimal places.) Step 3: Shade the area represented by the p- value, Step 4: Enter the p- value (Round to 3 decimal places.) (d) Based on your answer to part (c), choose what can be concluded, at the 0.05 level of significance, about the claim made by the salesperson. * 5 ? Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the coin lands on heads more than 74%% of the times it is flipped. Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the coin lands on heads more than 74% of the times it is flipped. Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the coin lands on heads more than 74%% of the times it is flipped. Since the p-value is greater than the level of significance, the null hypothesis is not rejected So, there is not enough evidence to support the claim that the coin lands on heads more than " of the times it is flipped
