Solution :
1) This is the two tailed test .
The null and alternative hypothesis is
H0 : p = 0.58
Ha : p 0.58
= 0.53
P0 = 0.58
1 - P0 = 1 - 0.58 = 0.42
Test statistic = z
=
- P0 / [
P0
* (1 - P0 ) / n]
= 0.53 - 0.58/ [(0.58
* 0.42) / 800]
Test statistic = z = -2.87
= 0.05
/2
= 0.025
Z/2
= Z0.025 ± 1.96
critical region = z <-1.96 or z > 1.96
Yes, because the test value -2.87 is in the critical region.
2) z = -1.63
P(z < -1.63) = 0.0516
This is the two tailed test
P-value = 2 * P(z < -1.63)
P-value = 2 * 0.0516
P-value = 0.1032
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