Question

A restaurant estimates that about 11% of its adult patrons are vegetarians. However, a national organization says the number of adult vegetarians is at least 12%. Suppose that you sample n = 600 adults and the number who indicate they are vegetarian is x = 48.

Find the test statistic and rejection region, using the α = 0.01 level of significance. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

Given:

H₀: p = 0.12 versus H_a: p < 0.12

test statisticz=??

rejection regionz>??

z<??

Answer 1

Solution :

The null and alternative hypothesis is

H0 : p = 0.12

Ha : p < 0.12

= x / n = 48 / 600 = 0.08

P0 = 0.12

1 - P0 = 1 - 0.12 = 0.88

Test statistic = z =

= - P0 / [P0 * (1 - P0 ) / n]

=0.08 - 0.12 / [(0.12 * 0.88) / 600]

Test statistic = z = -3.02

This is the left tailed test

= 0.01

P(z < z ) = 0.01

P(z < -2.33 ) = 0.01

z < -2.33