Sampling Distributions Acrobatiq Distribuciones DE Muestreo PDF

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Examen de la plataforma acrobatiq de la materia estadística inferencial...

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11/12/2020

Sampling Distributions | Acrobatiq

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DISTRIBUCIONES DE MUESTREO

SAMPLING DISTRIBUTIONS Paso 1 de 1

Based on the Journal of the American Medical Association, weights of all newborn babies in U.S. follow a normal distribution with a mean of 3420 grams and standard deviation of 500 grams. The weights of 625 randomly selected newborns were recorded and it was found that the average and standard deviation in this sample were 3450 grams and 490, respectively. Pregunta 1 de 13 Which of the following is a parameter?

500 3450 625 490 This is correct. 500 is the population standard deviation and therefore a parameter.

Pregunta 2 de 13 Processing math: 100%

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11/12/2020

Sampling Distributions | Acrobatiq

Which of the following is a statistic?

3420 500 625 3450 490 Both 3450 and 490 are statistics. This is correct. 3450 and 490 are the sample mean and sample standard deviation, respectively, and therefore both are statistics.

Pregunta 3 de 13 ,

,

, and

(in this order are):

3450, 3420, 490, 500 490, 500, 3450, 3420 500, 490, 3420, 3450 3420, 3450, 500, 490 3450, 625, 490, 500 This is correct.

Pregunta 4 de 13 Processing math: 100%

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11/12/2020

Sampling Distributions | Acrobatiq

Which of the following statements is consistent with the idea of sampling variability?

If we were to select a different random sample of 625 newborns we can expect that not all newborns will have the same weight. If we were to select a different random sample of 625 newborns, we can expect the mean and standard deviation in this sample to be different than the mean and the standard deviation in the first sample. If we were to select a different random sample of 625 newborns, the mean and standard deviation in this sample will be exactly the same as in the first sample -- 3450 and 490, respectively. If we were to select a different random sample of 625 newborns, the mean and standard deviation in this sample will be exactly the same as in the population – 3420 and 500, respectively This is correct. The idea of sampling variability is that no two random samples from the same population are identical. In other words, random samples vary.

It was reported that 30% of all credit card users in the U.S. pay their card card bill in full every month. Pregunta 5 de 13 A random sample of 21 credit card users is chosen. What is the mean and standard deviation of , the sample proportion of credit card users who pay their bill in full every month? (some answers are rounded).

Mean = 0.30, standard deviation = 0.1 Mean = 0.21, standard deviation = 0.1 Processing math: 100%

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11/12/2020

Sampling Distributions | Acrobatiq

Mean = 0.30, standard deviation = 0.01 Mean = 0.30, standard deviation = 0.065 Mean = 0.1, standard deviation = .30 This is correct. The mean is the population proportion p = 0.30 and the standard deviation is

Pregunta 6 de 13 Is it safe to assume that the sampling distribution of pˆ is approximately normal for random samples of size n=21?

Yes, since the sampling distribution of p ˆ is always normal. No, since n*p is not greater than 10. Yes, since n*(1-p) is greater than 10. No, since n=21 is not large than 30. This is correct.

Pregunta 7 de 13 It was reported that 30% of all credit card users in the U.S. pay their card card bill in full every month. A random sample of size n=84 credit cards users is chosen. Which of the following is true regarding the effect of the increased sample size (from 21 to 84) on the mean and standard deviation of sampling distribution of p^? Processing math: 100%

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11/12/2020

Sampling Distributions | Acrobatiq

The mean of the sampling distribution will stay the same, but the standard deviation will decrease. Both the mean and standard deviation of the sampling distribution decrease. Both the mean and standard deviation of the sampling distribution will not change. The mean of the sampling distribution will decrease, but the standard deviation will stay the same. The mean of the sampling distribution will stay the same, but the standard deviation will increase. This is correct.

Pregunta 8 de 13 There is 95% chance in a random sample of n=84 card users, the proportion of those who pay their bills in full every month will be:

Between .25 and .35 Between .20 and .40 Between .15 and .45 Between .10 and .50 We cannot answer this question since for n=84 we cannot safely assume that the sampling distribution is normal. This is correct. When n=84, the mean and standard deviation of the sampling distribution are: p = .30 and p(1-p)n=.3(1-.3)84=0.05 , respectively.

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11/12/2020

Sampling Distributions | Acrobatiq

By the standard deviation rule, there is 95% chance that the sample proportion will be within two standard deviations of its mean. In other words, between .30 – 2(.05) = .20 and .30 + 2(.05) = .40.

Pregunta 9 de 13 20% of all the students at a large university are international students. Two random samples of students are chosen; a random sample of n=64 students and a random sample of n=400 students. In which of the two samples is it more likely that more than 25% of the sampled students are international students?

Both samples have the same chance of having more than 25% international students since both are random samples from the same population. The sample of size n=64 since in there is more variability in the proportion of international students in smaller samples. The sample of size n=400 since there are more international students in a larger sample. The sample of size n=400 since in there is more variability in the proportion of international students in larger samples. This is correct.

Pregunta 10 de 13 In which of the following scenarios we cannot safely assume that the sampling distribution of the sample mean X¯is normal or approximately normal?

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11/12/2020

Sampling Distributions | Acrobatiq

The weight of the baggage checked by an individual passenger has mean μ=50 pounds and standard deviation σ=15 pounds. A random sample of n=75 passengers is selected and the average weight of their checked baggage, x¯, is determined. The weight of the baggage checked by an individual passenger has a normal distribution with mean μ=50 pounds and standard deviation σ=15 pounds. A random sample of n=75 passengers is selected and the average weight of their checked baggage, x¯, is determined. The weight of the baggage checked by an individual passenger has mean μ=50 pounds and standard deviation σ=15 pounds. A random sample of n=10 passengers is selected and the average weight of their checked baggage, x¯, is determined. The weight of the baggage checked by an individual passenger has a normal distribution with mean μ=50 pounds and standard deviation σ=15 pounds. A random sample of n=10 passengers is selected and the average weight of their checked baggage, x¯, is determined. This is correct. We can assume that the sampling distribution of the sample mean is normal (or approximately normal) as long as at least one of the following two conditions holds:

the variable of interest (weight in this case) is known to have a normal distribution in the population the sample size is large enough (n>30). In other words, the only case when we cannot assume that the sampling distribution of the sample mean is normal is when neither of the two conditions holds. In this case, we are not told that weights have anormal distribution and n=10...