A poll surveyed a random sample of 50 adults. The survey asked the following question: "Do you feel things are going well in the United States these days?" Assume the only answers are Yes or No. The results are in the table below.

No Yes No No Yes Yes No Yes No Yes

Yes No Yes No Yes No Yes No Yes No

Yes No Yes No Yes No Yes No Yes No

Yes No Yes No Yes No Yes No Yes No

No No No Yes No No No Yes Yes No

Find the sample proportion of those that said Yes. Round your answer to three decimal places as needed.

To determine the sample proportion of adults who answered "Yes", we first need to count the total number of "Yes" responses in the survey table. The survey includes 5 rows and 10 columns, giving us a total sample size of \(n = 5 \times 10 = 50\) responses. By carefully counting the occurrences of "Yes" in each row:

Row 1: 5 "Yes" responses
Row 2: 5 "Yes" responses
Row 3: 5 "Yes" responses
Row 4: 5 "Yes" responses
Row 5: 3 "Yes" responses

Summing these up, the total number of "Yes" responses is \(5 + 5 + 5 + 5 + 3 = 23\).

Calculate the sample proportion

The sample proportion \(\hat{p}\) is calculated by dividing the number of favorable responses (in this case, "Yes") by the total sample size \(n\). Using our counts:
\[\hat{p} = \frac{\text{Number of "Yes" responses}}{\text{Total sample size}} = \frac{23}{50}\]
To convert this fraction to a decimal, we perform the division:
\[\hat{p} = 23 \div 50 = 0.46\]
Since we are asked to round the answer to three decimal places if needed, we can write this as \(0.460\).

Final conclusion

After counting the responses and performing the division, we find that the sample proportion of adults who answered "Yes" is \(0.460\). Thus, the final answer is \(\boxed{0.460}\).

Examples

In social research, understanding public sentiment is crucial. If you conduct a survey and want to report the percentage of people who support a policy, you would use this exact method. By calculating the proportion of "Yes" answers, researchers can estimate the population's overall stance. For instance, if \(\hat{p} = 0.460\), you can conclude that \(46\%\) of the surveyed group feel things are going well.

No	Yes	No	No	Yes	Yes	No	Yes	No	Yes
Yes	No	Yes	No	Yes	No	Yes	No	Yes	No
Yes	No	Yes	No	Yes	No	Yes	No	Yes	No
Yes	No	Yes	No	Yes	No	Yes	No	Yes	No
No	No	No	Yes	No	No	No	Yes	Yes	No

No	Yes	No	No	Yes	Yes	No	Yes	No	Yes
Yes	No	Yes	No	Yes	No	Yes	No	Yes	No
Yes	No	Yes	No	Yes	No	Yes	No	Yes	No
Yes	No	Yes	No	Yes	No	Yes	No	Yes	No
No	No	No	Yes	No	No	No	Yes	Yes	No

No	Yes	No	No	Yes	Yes	No	Yes	No	Yes
Yes	No	Yes	No	Yes	No	Yes	No	Yes	No
Yes	No	Yes	No	Yes	No	Yes	No	Yes	No
Yes	No	Yes	No	Yes	No	Yes	No	Yes	No
No	No	No	Yes	No	No	No	Yes	Yes	No