I cannot figure out the P and Z please help

Question

In a certain school district, it was observed that 24% of the students in the element schools were classified as only children (no siblings).  However, in the special program for talented and gifted children, 90 out of 317 students are only children.  The school district administrators want to know if the proportion of only children in the special program is significantly different from the proportion for the school district. Test at the  level of significance.What is the hypothesized population proportion for this test? Correct(Report answer as a decimal accurate to 2 decimal places.  Do not report using the percent symbol.)Based on the statement of this problem, how many tails would this hypothesis test have?

Choose the correct pair of hypotheses for this situation:

Using the normal approximation for the binomial distribution (without the continuity correction), what is the test statistic for this sample based on the sample proportion?

 (Report answer as a decimal accurate to 3 decimal places.)You are now ready to calculate the P-value for this sample.P-value = (Report answer as a decimal accurate to 4 decimal places.)

Answer 1

Hello!

The value p is your sample proportion. When it's not given to you as a percentage, it will be given to you like it is in the question above. "90 out of 317 students are only children." This means your sample proportion is 90/317, so p≈0.2839

To find the z-score for this problem, you'll use the following formula:

(p-p₀)/(√[p₀*(1-p₀))/n]

Where p is the sample proportion, p₀ is the observed proportion, and n is the sample size.

In this case:

p=90/317≈0.2839

p₀=0.24

n=317

So z = (0.2839-0.24)/√[0.24(1-0.24)/317] ≈1.83

I hope that helps!