Question

Weekend birthdays Over the years, the percentage of births that are planned cesarean

sections has been rising. Because doctors can schedule these deliveries, there might be

more children born during the week and fewer born on the weekend than if births were

uniformly distributed throughout the week. To investigate, Mrs. McDonald and her class

selected an SRS of $73$people born since$1993$ . Of these people, $24$were born on Friday,

Saturday, or Sunday. To determine if these data provide convincing evidence that fewer than$43\%\left(\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$7$}\right.\right)$ of people born since $1993$were born on Friday, Saturday, or Sunday, $100$simulated SRSs were selected. Each dot in the graph shows the number of people that were born on Friday, Saturday, or Sunday in a simulated SRS of $73$people, assuming that each person

had a $43\%$chance of being born on one of these three days.

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 fewer than $43\%$of people born since $1993$were born on Friday, Saturday,

or Sunday? Explain your answer.

Short answer

a. The graph illustrates that the number of people who were born on Friday, Saturday or Sunday varies from $22to40$people.

b. NO, there is no convincing evidence that fewer than $43\%$of people born since $1993$were born on Friday, Saturday or Sunday

Step-by-step solution

Part (a): Step 1: Given information

It is given that to investigate children's birth days Mrs. McDonald and her class

selected an SRS of $73$people born since $1993$.

it is found that of these people, $24$were born on Friday, Saturday, or Sunday.

to check that these data provide strong evidence that fewer than $43\%\left(\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$7$}\right.\right)$of

people born since $1993$were born on Friday, Saturday, or Sunday, $100$simulated SRSs

were selected.

the below graph shows the data of people born on Friday, Saturday, or Sunday in a simulated SRS of $73$people, assuming that each person had a $43\%$chance of being born on one of these three days.

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

Part (a):Step 2: Explanation

Each dot in the above graph shows a random sample of $73$people

It is found that each of the samples does not have the same no. of people who were born on Friday, Saturday, or Sunday and this shows that there is sampling variability present among the different samples and the no. of people varies from $22$to$40$.

Part (b): Step 1: Given information

It is given that to investigate children's birth days Mrs. McDonald and her class

selected an SRS of $73$people born since $1993$.

it is found that of these people, $24$were born on Friday, Saturday, or Sunday.

to check that these data provide strong evidence that fewer than $43\%\left(\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$7$}\right.\right)$of

people born since$1993$were born on Friday, Saturday, or Sunday, $100$simulated SRSs

were selected.

the below graph shows the data of people born on Friday, Saturday, or Sunday in a simulated SRS of $73$people, assuming that each person had a $43\%$chance of being born on one of these three days.

b. we need to find is there convincing evidence that fewer than $43\%$of people born since $1993$were born on Friday, Saturday, or Sunday.

Part (b): Step 2: Explanation

From the data

$43\%$of the people is $43\%\times 73=.43\times 73=31.39\approx 31$

From the graph, we can say that there are $8$dots at $31$and this implies that $31$people were born on Friday, Saturday, or Sunday. but this does not show that fewer than $43\%$of people born since $1993$were born on Friday, Saturday, or Sunday, and this implies that there is no convincing evidence that fewer than $43\%$of people born since $1993$were born on Friday, Saturday or Sunday.