Question

Please use all 5 places of decimal when working with probabilities and please use at least 3 significant figures when dealing with proportions. For larger numbers, please use two places of decimal. Please show ALL work.

1. The proportion of students performing at grade level in NYC is 0.4 overall. A new school opens up and out of a random sample of 50 students, 25 are at grade level. Using a 99% confidence interval, test the hypothesis that the proportion of students at grade level in the new school is the same as the proportion of students at grade level in NYC.

Answer 1

P = Population Proportion = 0.4

Q = 1 - P = 0.6

n = Sample Size =50

p = Sample Proportion = 25/50 = 0.50000

SE =

=

V0.4 × 0.6/50= 0.06928

= 0.01

From Table, critical values of Z = 2.576

Confidence Interval:

0.50000 (2.576 X 0.06928)

=0.50000 0.17849

= ( 0.32151 , 0.67648)

Confidence interval:

0.32151 < P < 0.67648

Since 0 is not included in the confidence interval, the data does not support the claim that the proportion of students at grade level in the new school is the same as the proportion of students at grade level in NYC.