Question

You wish to test the following claim (Ha) at a significance level of α=0.01.

Ho:p=0.86

Ha:p>0.86

You obtain a sample of size n=351 in which there are 310 successful observations. For this test, you should use the (cumulative) binomial distribution to obtain an exact p-value. (Do not use the normal distribution as an approximation for the binomial distribution.)

What is the p-value for this sample? (Report answer accurate to four decimal places.)

p-value =

My main question is: How do i get the p-value from the TI-83 calculator? If not possible, then how do I do it by hand?

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.86

H_a : p > 0.86

n = 351

x = 310

= x / n = 310 / 351 = 0.8832

P₀ = 0.86

1 - P₀ = 1 - 0.86 = 0.14

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.8832 - 0.86 / [(0.86 * 0.14) / 351]

= 1.252

Test statistic = 1.25

P(z > 1.252) = 1 - P(z < 1.252) = 1 - .8947 = 0.1053

P-value = 0.1053