Question

I'm having a hard time figuring out how would I do these two problem on the calculator? Ti 83. What values do I plug in, and where?? Thanks!!

The state education commission wants to estimate the fraction of tenth grade students that have the reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.2; How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade reading level at 98% confidence level with an error of at most 0.03?

ALSO

NASA is conducting an experiment to find out the fraction of people who black out at G forces greater than 6. In an earlier study the population proportion was estimated to be 0.49. How large a sample would be required in order to estimate the fraction of people who black out at 6 or more Gs at the 80% confidence level with an error of at most 0.04?

Answer 1

n = z^2 pq/e^2

now here p = 0.2 , q = 1 - p = 0.8

e = 0.03

z for 98 % = 2.326348 which can be calculated from Ti-83

1) Access the invnorm function on the calculator by pressing 2nd
2)Then press VARS to access the DISTR menu.
3) You must choose the invnorm function

invnorm(0.99) will give z for 98 % confidence level

now just calculate n

= 2.326348^2 * 0.2 * 0.8/0.03^2

= 962.114669707

hence n = 963

2) similarly here z = invnorm(0.90) = 1.281552

n = 1.281552^2 * 0.49*0.51/0.04^2

= 256.518527

n = 257