Animal Hope is a non-profit rescue shelter in Fort Worth. Between March 7th and April 7th, assume that their website listed 89 dogs as available for adoption, and of those 17 were less than one year old. When considering the city of Fort Worth, it is known that 13% of all dogs available for adoption are less than one year old. Treat the dogs at Animal Hope as a random sample from all dogs available for adoption in Forth Worth. (*Round all calculated values to four decimals.*)What is the value of the true population proportion of adoptable dogs less than one year old

The true population proportion of adoptable dogs less than one year old in Fort Worth is given as 13% or 0.13. This is the value of the true population proportion, denoted as \( p \), based on the information provided about the entire population of adoptable dogs in the city.

Therefore, the value of the true population proportion \( p \) is:

\[
p = 0.13
\]

Would you like further details or any questions? Here are some related questions you may explore:

1. How can we calculate the sample proportion of dogs less than one year old at Animal Hope?
2. How would you test if the proportion of young dogs at Animal Hope is significantly different from the population proportion?
3. What statistical methods can be used to determine whether Animal Hope's proportion of young dogs differs from that of Fort Worth?
4. How would the margin of error for the sample proportion be calculated in this case?
5. What sample size would be required to achieve a certain level of confidence in estimating the population proportion?

**Tip:** When rounding to four decimal places, ensure to round off appropriately by looking at the fifth decimal for precision.

Animal Hope is a non-profit rescue shelter in Fort Worth. Between March 7th and April 7th, assume that their website listed 89 dogs as available for adoption, and of those 17 were less than one year old. When considering the city of Fort Worth, it is known that 13% of all dogs available for adoption are less than one year old. Treat the dogs at Animal Hope as a random sample from all dogs available for adoption in Forth Worth. (*Round all calculated values to four decimals.*) What is the value of the true population proportion of adoptable dogs less than one year old?

This problem explores how to find the true population proportion of adoptable dogs less than one year old in Fort Worth, using a sample of 89 dogs from Animal Hope. We use statistical concepts such as population proportion and sample proportion to solve the problem. Ideal for students in Grades 10-12.

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