Question

Can someone hlpe with questions A and/or B please

Answer 1

Let sample in Texas be p1, Louisiana be p2.
Null Hypothesis: 
p1 - p2 = 0
Alternative Hypothesis: (This represents the claim)
p1- p2 < 0

To calculate test statistic, you need the pooled estimate which is a weighted average of the 2 sample proportions.
$P = \frac{n_1 p_1 + n_2 p_2}{n_1 + n_2} = \frac{2000(.179+.265)}{2000+2000} = 0.222$
Next get standard error:
$SE = \sqrt{P(1-P)(\frac{1}{n_1} + \frac{1}{n_2})} = \sqrt{.222(1-.222)(\frac{1}{2000}+\frac{1}{2000})} = 0.01314$
Calculate test statistic:
$Z = \frac{p_1 - p_2}{SE} = \frac{.179 - .256}{.01314} = -5.86$
To find p-value, look up Z-value in standard normal table.
Anything smaller than -3 or larger than 3, you can estimate to have
p-value = 0.

If p-value < alpha, Reject Null Hypothesis.
For this example, 0 < 0.05, therefore reject null hypothesis.

There is evidence to support claim that proportion of smokers in Texas is LESS than Louisiana.