A manufacturer of bottled tea runs a promotion, where consumers can win a free bottle of tea if the cap of the bottle says "Winn
er.” The manufacturer claims that 1 in 5 bottles is a winner. Jack really likes the tea and has noticed that the last 10 bottles he has bought has not had a winner. Suspecting the manufacturer’s claim is false, Jack decides to select 10 bottles of tea from 10 randomly selected stores. He is surprised again when none of the 10 bottles is a winner. Assuming the manufacturer’s claim is true, Jack simulates 100 values of selecting winners in 10 bottles. The dotplot displays these simulated proportions. Using the dotplot and the proportion of winners in Jack’s sample, is there convincing evidence that the manufacturer’s claim is wrong?
Yes; because a proportion of 0 occurred 3 out of 100 times, the sample proportion of winners is statistically significant and there is convincing evidence that the manufacturer’s claim is false.
Yes; because a proportion of more than 0 occurred 97 out of 100 times, the sample proportion of winners is statistically significant and there is convincing evidence that the manufacturer’s claim is false.
No; because a proportion of 0 occurred 3 out of 100 times, the sample proportion of winners is not statistically significant and there is not convincing evidence that the manufacturer’s claim is false.
No; because a proportion more than 0 occurred 97 out of 100 times, the sample proportion of winners is not statistically significant and there is not convincing evidence that the manufacturer’s claim is false.
