Question

The city of Hamden received money for improvements of the town’s park. The park committee polled a random sample of 75 residents from the town. Of the 75 residents, 27 would like to see more trees planted in the park. From this information, what can be inferred?

Answer 1

Answer:

Step-by-step explanation:

Given that the proportion for the random sample of 75 residents from the town who would like to see more trees in the park is

$p=\frac{27}{75} =\frac{9}{25} \\

q=1-p=\frac{16}{25} \

\Mean of the sample proportion P = \frac{9}{25}\\

Std error of proportion =\sqrt{\frac{pq}{n} } \\

=\sqrt{\frac{9(16)}{25(25)(75)} }\\

=0.003072\\

Margin of error = 1.95(std error) = \\

=0.006$

We assumed 95% confidence level

The random sample gives an idea about the whole town preferences for trees planted

We have sample proportion as 0.36 and

confidence interval 95% =(0,36-0.006, 0.+0.006)

=(0.354,0.366)

We are 95% confident that when different samples for large sizes are taken, people who prefer trees to be planted would be within 0.354 and 0.366

or between 35.4% and 36.6%