First simulate the case for 80 random samples of 50 adults.
The company's claim is probably accurate.
Practice makes perfect
We are told that a national polling company asserts that 34 % of U.S adults say mathematics is the most valuable school subject in their lives. We survey a random sample of 50 adults. Then we will make a conclusion about the accuracy of the following claim .
The population proportion is 0.34 when 21 adults say mathematics is the most valuable school subject.
Therefore, we will create a simulation by using a random number generator on graphing calculator. We will choose 80 random samples of size 50. To generate the numbers we will press MATH. Then we will scroll to the right to the PRB menu and choose the fifth option, randInt(.
Then we will press ENTER. We want to select randomly 50 numbers from 0 to 99, and the numbers 1 through 34 will show the adults who say mathematics is the most valuable school subject. Therefore, we will write 0, 99, and 50, respectively after randInt(. Next, we will press ENTER to see the 50 random numbers.
When we scroll to the right we can see 50 generated numbers. Note that since the graphing calculator generates the numbers randomly, the generated set of numbers gives us a sample set. From here we will make a table and write the all generated numbers. Also, we will highlight the numbers 1 through 34.
In the table the numbers in the pink circles give us the number of adults who say mathematics is the most valuable school subject, which is 14 out of 50 adults. Now we will find the sample proportion.
14/50=0.28
Next, to analyze the claim we want to simulate the case by choosing 80 random samples of 50 people. Therefore, we will proceed in the same way 80 times. The result of each sample is as follows.
By using this information we will count the number of each proportion and draw a dot plot that shows the proportions of the adults who says mathematics is the most valuable subject.
Let's recall that in our claim we survey a random sample of 50 adults and 21 of them say mathematics is the most valuable school subject. Let's find its sample proportion.
21/50=0.42
From here we will look at how many time this result occurred in the simulation.
In the simulation 0.42 occurred 5 times in 80 samples. It is likely that 21 out of 50 adults say mathematics is the most valuable subject, as the company asserts 34 % of the adults say mathematics is the most valuable subject. Therefore, we can conclude that the claim of the company is probably accurate.
