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Morgarella [4.7K]
4 years ago
9

A polling firm would like to estimate the proportion of registered Fort Collins voters who plan to vote in the upcoming city ele

ctions. Using voter registration records, they randomly sample 300 names and mail surveys to the selected voters' home addresses. Of the surveys they mail out, they receive 68 back. The survey has one question that reads as follows: "Which of the following describes how likely you are to vote next year in next year's mid-term elections: Definitely not voting, not likely to vote, likely to vote, or definitely voting?" For each question below, fill in the blank using the best answer from the pull-down menu. You have two attempts per question. The group of all registered voters in Fort Collins is the of interest. The survey respondent's answer to the italicized question above is the of interest. Suppose we calculate the proportion of voters from our sample who say they are definitely voting. This proportion is an example of a/an. Suppose we are interested in estimating the proportion of voters in Fort Collins who will definitely be voting. This proportion is an example of a/an: Each individual person in our sample is considered to be a/an: If the people who returned the surveys did so for a reason that is related to their likelihood of voting, then there might be in our sample. When we use the results of our sample to make a claim about all voters in Fort Collins, we are engaging in statistical
Mathematics
1 answer:
Scorpion4ik [409]4 years ago
6 0

Answer:

sdStep-by-step explanation:

d

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Answer:

Check explanation below.

Step-by-step explanation:

Hello!

The objective of this experiment is to test if doctor Doom is controlling the neighbors' minds from his new Lair. To test this a random sample of 11 neighbors was taken and a "free will" test was administrated before the Villain's Lair was constructed and again after it was finished.

This experiment type where you have a single sample and the variable is measured "before" and "after" applying a treatment (in this case, that doctor Doom has moved into town) is a classic example of a paired sample test. You have two dependent variables, X₁: "Results of the free will test before Dr. Doom Lair is constructed" and X₂: "Results of the free will test after Dr. Doom Lair is constructed", with these variables you can establish a new variable, Xd, that I'll define as " X₁- X₂", and the objective of my hypothesis test will be to know if there is any change after the Lair is done, if there is, in fact, a change then the population mean of the difference will be nonzero, symbolically: μd ≠ 0

Using the data I've calculated the summary measures for Xd:

sample mean: Xd[bar]= 3.18

sample standard deviation: Sd= 5.44

The statistic hypothesis is:

H₀: μd = 0

H₁: μd ≠ 0

α: 0.05

(There is no signification level specified, so I've chosen the most common one)

Assuming that the variable difference, Xd, has a normal distribution, and with unknown population variance, the best statistic to use is the Students-t for paired samples:

t=  Xd[bar] - μd  ~t_{n-1}

Sd/√n

This test is two-tailed, so you will reject at low values of the statistic or at high values of it.

t_{n-1;\alpha/2 } = t_{10; 0.025} = -2.228

t_{n-1; 1-\alpha /2} = t_{10; 0.975} = 2.228

If t ≤ -2.228 or t ≥ 2.228 then you reject the null hypothesis.

If -2.228 < t < 2.228 then you don't reject the null hypothesis.

t= <u> Xd[bar] - μd  </u> =  <u> 3.18 - 0  </u> = 1.94

        Sd/√n             5.44/√11

Since the statistic value t= 1.94 then the decision is to not reject the null hypothesis.

So, with a significance level of 5% there is not enough evidence to reject the null hypothesis, this means that the population mean of the difference on the free will test results of the neighbors before and after the Villain's Lair was constructed is equal to cero. In other words, there is not enough evidence to conclude that Dr. Doom is controlling the neighbor's minds.

I hope it helps!

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Answer:

the answer is D

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