AnswersNC-Math 4Sampling Distributions – Center and Variability

Sampling Distributions – Center and Variability Answers

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The owner of an apple orchard knows that the average weight of Granny Smith apples is 380 grams. A random sample of 40 apples was selected and the mean weight was calculated. Let μ = the true mean weight of the Granny Smith apples in the orchard. Which of the following means is least likely to occur if the true mean weight is 380 grams?

A
300 grams
B
350 grams
C
400 grams
D
450 grams
2
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A statistics teacher has a large container of beads that she says contains 60% blue beads. A student randomly selects 50 beads. Let p = the true proportion of blue beads in the container. If the true proportion of blue beads is 0.60, which value of is least likely to occur?

Question illustration
A
0.50
B
0.60
C
0.70
D
0.80
3

The ages of the 5 officers for a school club are 18, 18, 17, 16, and 15. The median of the ages of the officers is 17.0. The table displays all possible samples of size 2 and the corresponding median for each sample.Using the medians in the table, is the sample median an unbiased estimator?

Question illustration
A
Yes, 50% of the sample medians are 17 or more, and 50% are below.
B
Yes, the mean of the sample medians is 16.8, which is the same as the mean age of the officers.
C
No, the mean of the sample medians is 16.8, which is not the same as the median age of the officers.
D
No, the median of the sample medians is 16.75, which is not the same as the median age of the officers.
4

The ages of the 5 officers for a school club are 18, 18, 17, 16, and 15. The standard deviation of the distribution of ages is 1.17. The table displays all possible samples of size 2 and the corresponding ranges for each sample.Using the values in the table, is the sample standard deviation an unbiased estimator?

Question illustration
A
Yes, 50% of the standard deviations are above 1.17, and 50% are below 1.17.
B
Yes, the mean of the sample standard deviations is 1.13, which is only 0.04 less than the population value, 1.17.
C
No, the mean of the sample standard deviations is 1.13, which is not the same as 1.17.
D
No, the standard deviation of the sample standard deviations is 0.68, which is not the same as 1.17.
5

A student decides to spin a dime and determine the proportion of times it lands on heads. The student spins the dime 25 times and records that it lands on heads 17 times. He decides to spin the dime again and spins it 100 times. Which of the following is a correct statement about the variability of the sampling distribution?

A
Since the sample size is increased, the variability will increase.
B
Since the sample size is increased, the variability will decrease.
C
Since the sample size is increased, the variability of the population will increase.
D
Since the sample size is increased, the variability of the population will decrease.
6

A farmer determines that, on average, his chickens lay a total of 16 eggs each day. A random sample of 10 days was taken, and the mean number of eggs was 15.1 eggs. Let μ = the true mean number of eggs the chickens lay each day. Under the assumption that the true mean number of eggs is 16, 100 simulated means for samples of size 10 are shown in the dotplot.Using the dotplot, is there evidence that the chickens are laying fewer than 16 eggs?

Question illustration
A
Yes, since a sample mean number of eggs of 15.1 eggs or less only occurred twice in simulated values, there is evidence that the true mean number of eggs is less than 16.
B
Yes, since a sample mean number of eggs of 15.1 is less than the mean number of eggs of 16, there is evidence to prove that the true mean number of eggs is less than 16.
C
No, since a sample mean number of eggs of 15.1 is only 0.9 eggs less than a mean number of eggs of 16, there is insufficient evidence that the true mean number of eggs is less than 16.
D
No, since a sample mean number of eggs of 15.1 never occurred in the dotplot, it is not possible that a random sample of 10 eggs will have a mean number of eggs of 15.1. Therefore, there is insufficient evidence that the true mean number of eggs is less than 16.
7

A statistics teacher has a large container of beads that she says contains 60% blue beads. A student randomly selects 50 beads. Let p = the true proportion of blue beads in the container. Under the assumption that the true proportion is 0.60, the student generated 200 values of .What does the dot above 0.74 represent?

Question illustration
A
There is a 1 in 200 chance that the true proportion of blue beads is 0.74.
B
In one simulated sample of 50 beads the proportion of blue beads is 0.74.
C
There is a 1 in 200 chance that the sample proportion of blue beads is 0.74.
D
In one simulated sample of 50 beads the true proportion of blue beads is 0.74.
8

A statistics teacher has a large container of beads that she says contains 60% blue beads. A student randomly selects 50 beads, and 25 of them were blue. Let p = the true proportion of blue beads in the container. Under the assumption that the true proportion is 0.60, the student generated 200 values of .Is there evidence that the true proportion of blue beads in the container is less than 0.60?

Question illustration
A
Yes, a proportion of 0.5 proves that the true proportion of blue beads in the container is less than 0.6.
B
Yes, a proportion of 0.5 only occurred 5 times out of 200 simulated proportions; therefore, there is sufficient evidence that the true proportion of blue beads in the container is less than 0.6.
C
No, a proportion of 0.5 is only 0.1 less than a proportion of 0.6; therefore, there is insufficient evidence that the true proportion of blue beads in the container is less than 0.6.
D
No, a proportion of 0.5 or less occurred 16 times out of 200 simulated proportions; therefore, there is insufficient evidence that the true proportion of blue beads in the container is less than 0.6.
9

A farmer determines that, on average, his chickens lay a total of 16 eggs each day. A random sample of 10 days was taken, and the mean number of eggs was determined. Let μ = the true mean number of eggs the chickens lay each day. Which of the following values for the sample mean is the least likely to occur?

A
15
B
16
C
17
D
18
10

The owner of an apple orchard knows that the average weight of Granny Smith apples is 380 grams. Which of the following sample sizes would have the greatest variability?

A
20
B
25
C
30
D
35

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