Question

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 $\raisebox{1ex}{$83$}\!\left/ \!\raisebox{-1ex}{$124$}\right.$$\left(66.9\%\right)$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.

Short answer

a. The graph shows that the simulated number of right-tilting couples ranges from $45to76$.

b. Yes, there is convincing evidence that couples prefer to kiss the " right way "

Step-by-step solution

Part (a): Step 1: Given information

It is given that according to a random sample of $124$kissing couples, it is found that $\raisebox{1ex}{$83$}\!\left/ \!\raisebox{-1ex}{$$}\right.124$$\left(66.9\%\right)$couples tilted to the right.

To check that these data provide convincing evidence $100$simulated $SRSs$were selected.

the dot in the below graph shows the no. of couples tilted to the right while kissing, assuming that each couple has a $50\%$chance of tilting to the right.

a. we need to find how the graph illustrates the concept of sampling variability.

Part (a): Step 2: Explanation

From the graph, we found that each of the samples does not have the same simulated no. of couples who tilt to the right, which shows that there is sampling variability present in the samples.

Part (b): Step 1: Given information

It is given that according to a random sample of $124$kissing couples, it is found that $\raisebox{1ex}{$83$}\!\left/ \!\raisebox{-1ex}{$124$}\right.$$\left(66.9\%\right)$couples tilted to the right.

To check that these data provide convincing evidence $100$simulated $SRSs$were selected.

the dot in the below graph shows the no. of couples tilted to the right while kissing, assuming that each couple has a $50\%$chance of tilting to the right.

b. we need to check that is there any convincing evidence that couples prefer to kiss the right way.

Part (b): Step 2: Explanation

It is given that $83$of the $124$couples tilted to the right

from the graph, we found that $83$lies on the rightmost side of the dot plot, and in the graph largest dot present on the $76$and $83$is higher than $76$.

then this implies that if each couple had a $50\%$chance of tilting to the right then it is very unlikely that there are $83$couples who tilted to the right and thus we can say that couples tend to prefer to kiss the "right way".