Question

1. kissing the right way according to a newspaper article, “most people are kissing the ‘right way.’” that is, according to a study, the majority of couples prefer to tilt their heads to the right when kissing. in the study, a researcher observed a random sample of 124 kissing couples and found that 83/124 (66.9%) of the couples tilted to the right. to determine if these data provide convincing evidence that couples are more likely to tilt their heads to the right, 100 simulated srss were selected. each dot in the graph shows the number of couples that tilt to the right in a simulated srs of 124 couples, assuming that each couple has a 50% chance of tilting to the right. (a) explain how the graph illustrates the concept of sampling variability. (b) based on the data from the study and the results of the simulation, is there convincing evidence that couples prefer to kiss the “right way”? explain your answer.

Explanation:

(a) Sampling variability is shown as the simulated number of couples tilting right varies across 100 samples. Each dot represents a different simulated SRS result, indicating that sample - statistics can differ from sample to sample even when the true probability is 50%.
(b) In the study, 83 out of 124 couples tilted right. In the simulations (assuming 50% chance of tilting right), most of the simulated values are below 83. This suggests that getting 83 or more couples tilting right is unlikely under the 50% chance assumption. So, there is convincing evidence that couples prefer to kiss the "right way".

Answer:

(a) The graph shows different numbers of couples tilting right in 100 simulated SRSs, demonstrating that sample - statistics vary from sample to sample.
(b) Yes, there is convincing evidence. The observed number of couples tilting right in the study is much higher than what is typically seen in the simulations assuming a 50% chance.