SOLUTION: the department of health claims that less than 30% of South African adults smoke. From a sample of 5000 South African adults it was found that 1450 smoke. use 10% significance leve

Question 1160869: the department of health claims that less than 30% of South African adults smoke. From a sample of 5000 South African adults it was found that 1450 smoke. use 10% significance level and answer the following questions:
a) formulate a suitable hypothesis.
b) calculate a suitable test statistic.
c) calculate the p-value.
d) decide whether the department's claim is true.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
p hat=1450/5000=0.29 the proportion
Ho: p <=0.30
Ha: p>0.30
alpha=0.10 p{reject Ho|Ho true}
test stat is a z
reject for z>1.645 (which it won't be in this instance)
calculation z=(0.29-0.30)/sqrt(.3*.7/5000)
=-0.01/0.0065
=-1.54
fail to reject Ho (which one would given that result was consistent with Ho).
p-value is 0.94
Claim is not rejected (better than saying it is true, but there is certainly no evidence here to refute it).

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