A survey of 80 homes in a Washington D. C. suburb showed that 45 were air conditioned. A sample of 120 homes in a Pittsburgh suburb showed tht 63 had air conditioning. At α = 0.05, is there a difference in the two proportions? Please show all 4 steps of the classical approach clearly.

There is no significant difference between the two proportions

Step-by-step explanation:

State the hypotheses:

Null hypothesis -> H0: P1 = P2

Alternative hypothesis -> H1: P1 not = P2

Note that hypotheses constitute a two-tailed test. the null hypothesis will be rejected if the proportion from population 1 is too big or if it is too small.

Formulate an analysis plan

For the analysis, the significance level is 0.05. The test method is a two-proportion z-test.

Analyze sample data.

Using sample data we calculate the pooled sample porportion (p) and the standard error (SE). Using those measures, we compute the  z-score test statistic (z).

p = (p1*n1 + p2*n2)/(n1 + n2)

p1 = 45/80 = 0.5625

p2 = 63/120 = 0.525

n1 = 80

n2 = 120

p = (0.5625*80 + 0.525*120)/(80 + 120)

p = 0.54

SE = 0.07112

z = (p1 - p2)/ SE

z = (0.5625 - 0.525)/0.07112

z = 0.527

For z = 0.527 we have p-value 0.198

Interpret results. Since p - Value (0.198) of the test is greater than the alpha-0.05 (For two tailed test α-0.025). Therefore we cannot reject the null hypothesis.

There is no significant difference between the two proportions

a. the are of the rectangle is 18.25

b. 18.25 times two is 36.50

rae me : d

341

step-by-step explanation:

all you have to do is 9x31 (which equals 279) and then 20x31 (which equals 620). then you have to subtract. 620-279=341.