Solution :
This is the two tailed test .
The null and alternative hypothesis is
H0 : p = 0.30
Ha : p 0.30
= 0.37
P0 = 0.30
1 - P0 = 1 - 0.30 = 0.70
= 0.02
/2 = 0.01
Z/2 = Z0.01 ± 2.33
z critical left = z <-2.33
z critical right = z > 2.33
Test statistic = z=
= - P0 / [P0 * (1 - P0 ) / n]
= 0.37 - 0.30/ [(0.30 * 0.70) / 410 ]
Test statistic = z observed = 3.09
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