How to state null and alternative hypotheses for one and two-sided tests 
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Here are some of the hypothesis statements, I don't know why do cases (i),(j) null hypothesis would not be another way around, and they also contradict to the case (b),(f)
Any ideas on how to correctly states the null and alternative hypotheses? Appreciate for any comments

(i) If you take the alternative hypothesis to be
$H_a: p < 0.11,$ and you reject $H_0: p = 0.11$ or
$H_0: p \ge 0.11$ at the 5% level, then it is because
your sample proportion $\hat p$ of women developing breast
cancer is sufficiently below $0.11$ to be called
'significantly' below $0.11$ at the 5% level. This would
support the claim made in the text version of part (i).
Example: Perhaps you have $n = 1000$ women in your sample, of whom 87 developed breast cancer. Then the null distribution is $\mathsf{Binom}(n=1000,p=0.11)$ and $\hat p = 87/1000 = 0.087 < 0.11.$
Moreover, the P-value of an
exact binomial test would be $0.01977 < 0.05 = 5\%$
so we could reject $H_0$ at the 5% level and say that
$\hat p$ is significantly below $0.11$ at the 5% level
of significance. (In fact, the P-value is sufficiently small to claim significance at the 1% level. [Computations in R.]
pbinom(87, 1000, .11)  # binomial CDF
[1] 0.009771923

Roughly speaking, you might say that the 'critical value'
for this left-sided test at (about) the 5% level is $c=93,$
so that any number of breast cancer cases 83 or fewer out of the 1000 subjects would lead to rejection on $H_0$ at the 5% level (and any number of cases 87 or below would
lead to rejection at the 1% level).
qbinom(.05, 1000, .11)  # quantile function
[1] 94
pbinom(94, 1000, .11)   # CDF
[1] 0.0562174
pbinom(93, 1000, .11)
[1] 0.04521503

qbinom(.01, 1000, .11)
[1] 88
pbinom(87, 1000, .11)
[1] 0.009771923

The figure below shows the null distribution with a vertical dotted line at the 5%
critical value for a left=tailed test.

R code for figure:
x = 0:200;  PDF = dbinom(x, 1000, .11)
plot(x, PDF, type="h", col="blue", 
      main="Null Distribution")
abline(h=0, col="green2")
abline(v=0, col="green2")
abline(v=93.5, col="red", lwd=2, lty="dotted")

