Question

HELP PLS!!POINTS!!! A​ state-by-state survey found that the proportions of adults who are smokers in state A and state B were ​25.2% and ​20.6%, respectively.​ (Suppose the number of respondents from each state was ​2000.) At ​a=0.01, can you support the claim that the proportion of adults who are smokers is greater in state A than in state​ B? Assume the random samples are independent. Complete parts​ 1 through 4. (I have similar questions on my page if you could help me out!! Thank u!!)

Part 1)
Identify the claim and state H0 and Ha.
The claim is​ "the proportion of adults who are smokers in state A is
▼
the same as
greater than
different than
lower than
the proportion of adults who are smokers in state​ B."

Let p1 and p2 be the two population proportions. State H0 and Ha .

Part 2)

Find the critical​ value(s) and identify the rejection​ region(s).
Z0=?

Identify the rejection​ region(s).

Part 3)
Find the standardized test statistic.
z=?

Part 4)
Decide whether to reject or fail to reject the null hypothesis.

Interpret the decision in the context of the original claim.
Choose the correct answer below.
A. At the ​1% significance​ level, there is sufficient evidence to reject the claim.
B. At the ​1% significance​ level, there is insufficient evidence to reject the claim.
C. At the 1​% significance​ level, there is sufficient evidence to support the claim.
D. At the ​1% significance​ level, there is insufficient evidence to support the claim.

Answer 1

Part 1:

The claim is that the proportion of adults who are smokers in state A is greater than the proportion of adults who are smokers in state B.

H0: p1 <= p2

Ha: p1 > p2

Part 2:

We will use a significance level of a = 0.01. Since we are testing whether p1 > p2, this is a right-tailed test.

Using a normal distribution with a mean of 0 and a standard deviation of 1, we can find the critical value:

Z0 = invNorm(0.99) = 2.326

The rejection region is z > 2.326.

Part 3:

We can use the formula for the test statistic:

z = (p1 - p2) / sqrt(p*(1-p)*(1/n1 + 1/n2))

where p = (x1 + x2) / (n1 + n2), x1 and x2 are the number of smokers in state A and state B, respectively, and n1 and n2 are the sample sizes.

p1 = 0.252, p2 = 0.206, n1 = n2 = 2000

p = (x1 + x2) / (n1 + n2) = (0.252*2000 + 0.206*2000) / (2000 + 2000) = 0.229

z = (0.252 - 0.206) / sqrt(0.229*(1-0.229)*(1/2000 + 1/2000)) = 7.17

Part 4:

Since the test statistic z = 7.17 is greater than the critical value Z0 = 2.326, we reject the null hypothesis.

Therefore, at the 1% significance level, there is sufficient evidence to support the claim that the proportion of adults who are smokers is greater in state A than in state B.