At a magic shop, the salesperson shows you a coin that she says will land on heads more than 77% of the times it is flipped. In an attempt to convince you she's correct, the salesperson asks you to try the coin yourself. You flip the coin 70 times. (Consider this a random sample of coin flips.) The coin lands on heads 58 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 77%. (a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test. Ho: D 6 H₁: 0 Standard Normal Distribution р Explanation □口 O Et VE Check X EPID • The value of the test statistic is given by z = OSO (b) For your hypothesis test, you will use a Z-test. Find the values of np and n (1-p) to confirm that a Z-test can be used. (One standard is that np ≥ 10 and n (1-p) ≥ 10 under the assumption that the null hypothesis is true.) Here is the sample size and p is the poration proportion you are testing. np = 0 S n(1-p) = [ X = (c) Perform a Z-test. Here is some information to help you with your Z-test. 20.05 is the value that cuts off an area of 0.05 in the right tail of the distribution. 00 5 VE □口 р-р p(1-p) n 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use Privacy Center | Accessibility Aa 65°F C Standard Normal Distribution Step 1: Select one-tailed or two-tailed. One-tailed Two-tailed Step 2: Enter the critical value(s). (Round to 3 decimal places.) Step 3: Enter the test statistic. (Round to 3 decimal places.) 3 Explanation 2 Et 10 Check 0.3+ O Since the value of the test statistic lies in the rejection region, the null hypothesis is rejected. So, there is enough evidence to support the claim that the coin lands on heads more than 77% of the times it is flipped. EPIC 0.1+ (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. O Since the value of the test statistic lies in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the coin lands on heads more than 77% of the times it is flipped. 9+ 1 O Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is rejected. So, there is enough evidence to support the claim that the coin lands on heads more than 77% of the times it is flipped. O Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the coin lands on heads more than 77% of the times it is flipped. 2 S NEXT 3 2022 McGraw Hill LLC. All Rights Reserved. X Terms of Use | Privacy Center Accessib