Question

A student polls his school to see if students in the school district are for or against the new legislation regarding school uniforms. She surveys 600 students and finds that 480 are against the new legislation.

Answer 1

The subject is Mathematics at the High School level. A 90 percent confidence interval for the true proportion of students against the new school uniform legislation is calculated using the sample proportion and the standard error, multiplied by the z-score for the desired confidence level.

Step-by-step explanation:

The survey conducted by the student at her school regarding the new legislation on school uniforms involves the subject of Mathematics, specifically statistics. To calculate a 90 percent confidence interval for the true percentage of students who are against the new legislation, you can use the formula for a confidence interval for a population proportion.

The student found that 480 out of 600 students are against the new legislation. This means that the sample proportion (p) is 480/600 = 0.8 or 80%. To compute the confidence interval, use the following steps:

1. Find the standard error (SE) of the sample proportion, which is the square root of (p*(1-p)/n), where p is the sample proportion and n is the sample size.
2. Find the z-score corresponding to the desired confidence level (90%). You can find this value in a standard z-table.
3. Multiply the z-score by the SE to determine the margin of error (ME).
4. Add and subtract the ME from the sample proportion to find the lower and upper bounds of the confidence interval.

Interpreting the confidence interval means that we can be 90% confident that the true proportion of students who are against the new legislation lies within the calculated interval.