Chapter 22 Comparing Two Proportions. Comparing Two Proportions. Comparisons between two percentages are much more common (and interesting) than questions about isolated percentages.
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Comparing Two Proportions
Suppose you are interested in
whether men and women differ with
regard to how often they wash their
hands in public restrooms?
Two empty fields are used as parking lots for concerts and festivals. The number of vehicles that can park in Lot A has a mean of 219 and standard deviation of 13. Lot B can hold an average of 193 cars with a standard deviation of 11.
a. What is the expected difference for the number of vehicles parked in the two lots.
b. Find the standard deviation of that difference.
We are ___% confident that the
true proportion of [p1 in context]
is between ___% and ___%
[more/less] than the proportion of
[p2 in context].
Suppose you are interested in whether men and women differ with
regard to how often they wash their hands in public restrooms?
Researchers monitored the behavior of public restroom users at
major venues such as Turner Field and Grand Central Station and
found that 2393 out of 3206 men washed their hands and 2802 of
3130 women washed their hands. Create a 95% confidence interval
to describe the difference.
At Community Hospital, the burn center is experimenting with a new plasma compress treatment. A random sample of 316 patients with minor burns received the plasma compress treatment. Of these patients, it was found that 259 had no visible scars after treatment. Another random sample of 419 patients with minor burns received no plasma compress treatment. For this group, it was found that 94 had no visible scars after treatment. What is a 95% confidence interval of the difference in proportion of people who had no visible scars between the plasma compress treatment & control group?
pT: proportion of ppl who received plas comp treatment & had no visible scars
pN: proportion of ppl who did NOT receive plas comp treat & had no visable scars
Since these are all burn patients (come from the same pop.), we can add 316 + 419 = 735.
If not the same – you MUST list separately.
We are 95% confident that the true proportion of people who received plasma compress treatment and had no visible scars was between 53.7% and 65.4% more that the proportion of those who didn’t receive the treatment.
H0: p1 = p2
H0: p1 - p2 = 0
Ha: p1 - p2 > 0
Ha: p1 - p2 < 0
Ha: p1 - p2 ≠ 0
Be sure to define both p1 & p2!
Ha: p1 > p2
Ha: p1 < p2
Ha: p1 ≠ p2
If the numbers of successes are not whole numbers, round them first. (This is the only time you should round values in the middle of a calculation.)
p1 – p2 =0
A forest in Oregon has an infestation of spruce moths. In an effort to control the moth, one area has been regularly sprayed from airplanes. In this area, a random sample of 495 spruce trees showed that 81 had been killed by moths. A second nearby area receives no treatment. In this area, a random sample of 518 spruce trees showed that 92 had been killed by the moth. Do these data indicate that the proportion of spruce trees killed by the moth is different for these areas?
pu : the proportion of trees killed by moths in the untreated area
α = .05
P-value = 0.5547
Since p-value (.5547) > a(.05), I fail to reject H0. There is not sufficient evidence to suggest that the proportion of spruce trees killed by the moth is different for the treated and untreated areas.