Question

One study based on responses from 1018 randomly selected teenagers concluded that 41% of teenagers cite grades as their greatest source or pressure. Use. 0.05 signifciance level to test the claim that fewer than half of all teenagers in the population feel that greades are their greatest source of pressure.

Write the null and alternative hyptohesis

Find the test statisitc z=

Find the P-value for the found test statistic p:

State the conlcudion

reject or do not reject and why

Answer 1

Solution :

Given that,

n = 1018

= 41% = 0.41

P₀ = 0.5

1 - P₀ = 1 - 0.5 = 0.5

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.41 - 0.5 / [(0.5 * 0.5) / 1018]

= -5.74

Test statistic = -5.74

This is the left tailed test .

P(z < -5.74) = 0

P-value =0

= 0.05

P value <

Reject the null hypothesis .