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 = (n_1 p_1 + n_2 p_2)/(n_1 + n_2) = (2000(.179+.265))/(2000+2000) = 0.222`
Next get standard error:

`SE = \sqrt{P(1-P)((1)/(n_1) + (1)/(n_2))} = \sqrt{.222(1-.222)((1)/(2000)+(1)/(2000))} = 0.01314`
Calculate test statistic:

`Z = (p_1 - p_2)/(SE) = (.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.