Question

1. Determine if all of the conditions have been met for the following hypothesis tests. If so, write the hypotheses and identify the claim. (Do not conduct a full hypothesis test.)
(2 points for checking conditions and 2 points for hypotheses)

a. The Pew Research Center conducted a survey of 500 adults and found that 429 of them know what Twitter is. Use a 0.01 significance level to test the claim that at least 80% of adults know what Twitter is.

Answer 1

a)

Conditions for one-sample proportion z-test, are as follows,

1) The sample must be randomly selected from population.

here sample is randomly selected.

2) The population must be  at least 10 times as larger than sample.

here population is large hence, this condition also met.

3) n * p 10 and n * (1−p) 10 should be met.

here,

n * p 10 = 500 * 0.80 = 400 10 and

n * (1−p) 10 = 500 * ( 1 - 0.80)= 100 10

Hence, this condition also met.

Thus all above conditions met.

b)

hypothesis is as follows,

Ho : P 0.80

Ha : P < 0.80

the claim is null hypothesis.( Ho : P 0.80 )