Question

Test the hypothesis using the​ P-value approach. Be sure to verify the requirements of the test. Upper H 0 : p equals 0.62 versus Upper H 1 : p less than 0.62 n equals 150 comma x equals 81 comma alpha equals 0.01 Is np 0 left parenthesis 1 minus p 0 right parenthesis greater than or equals 10​? No Yes Your answer is correct. Use technology to find the​ P-value. ​P-value= nothing ​(Round to three decimal places as​ needed.)

Answer 1

Solution :

This is the less tailed test .

The null and alternative hypothesis is

H₀ : p = 0.62

H_a : p < 0.62

= x / n = 81 / 150 = 0.54

P₀ = 0.62

1 - P₀ = 0.38

np 0 left parenthesis 1 minus p 0 right parenthesis greater than or equals 10​ .

Yes

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.54 - 0.62 / [(0.62 * 0.38) / 150]

= -2.02

P(z < -2.02) = 0.0217

P-value = 0.0217

= 0.01

P-value >

Fail to reject the null hypothesis .