We want to test whether the true proportion of the population that believes Elvis Presley is still alive is less than 10%.The hypotheses are :
H0 : p = 0.1
H1 : p < 0.1
Here, n = 1248 and the sample proportion , = 8 % = 0.08
alpha = 0.01
The test statistic , z = ( - p) / {p(1-p)/n}
= -0.02 / 0.0085
= -2.35
At alpha 0.01 , z(critical) = -2.33
Therefore, decision rule is reject H0 if z < -2.33.
Here, z = -2.35 and hence,z < z(critical). We reject the null hypothesis at alpha = 0.01.
We conclude that the true proportion of the population that believes Elvis Presley is still alive is less than 10%.
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