## Is this correct?

Hi, I have 2 questions I'm not sure of.

1.) According to a 1997 study, 29.3% of self- employed persons worked on their home based businesses 35 hours or more each week. What is the probability that at least 30.5% of 800 people randomly sampled from the study's population worked on their businesses no less than 35 hours each week in 1997?

A) 0.2266
B) 0.2734
C) 0.3050
D) 0.7500

I chose answer C because .305/800=244. 244/800 is equal to 0.3050

2.) The commissioner of the state police is reported as saying that about 10% of reported auto thefts involve owners whose cars haven't really been stolen. What null hypotheses would be appropriate in evaluating this statement made by the commissioner?

A) Ho:u = 0.10 and H1:u1 is not equal to 0.10

B) Ho:u less than or equal to 0.10 and H1:u greater than or equal to 0.10

C) Ho:u greater than or equal to 0.10 and H1:u less than or equal to 0.10

D) Ho:u greater than 0.10 and H1:u less than or equal to 0.10

I chose answer A because the alternative hypothesis can have not equal to, less than or greater than. The alternative hypothesis can never have equal to as part of its statement. Is this correct? I know the answer is not D. Either 10% of the cars are stolen, or 10% of the car are not stolen.