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ISU Stats 101 Chapter 15II
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Diamond size is measured in carats. For ladies diamond rings, it is known the mean diamond size is 0.2 carats with a standard deviation of 0.057 carats. A company collected a random sample of 48 ladies diamond rings from all diamond companies and found these diamonds had a mean size of 0.204 carats.Select the correct description of the population in this study.
All diamonds found in ladies diamond rings
The Foley Products Company has designed a new blend of concrete they believe will be twice as strong as their current high quality concrete. This new blend of concrete is believed to produce batches with a population mean strength of 15,000 psi and a population standard deviation of 2,000 psi. To validate this belief, they collect a random sample of 49 concrete batches out of all the batches produced at their plant in a particular week. The mean strength of the random sample of 49 concrete batches is measured to be 14,731 psi.Select the correct description of the population in this study.
All the batches of the new blend of concrete made at their plant in a particular week
The Foley Products Company has designed a new blend of concrete they believe will be twice as strong as their current high quality concrete. This new blend of concrete is believed to produce batches with a population mean strength of 15,000 psi and a population standard deviation of 2,000 psi. To validate this belief, they collect a random sample of 49 concrete batches out of all the batches produced at their plant in a particular week. The mean strength of the random sample of 49 concrete batches is measured to be 14,731 psi.Select the correct description of the population mean in this study.
The mean strength of all batches of the new blend of concrete produced at their plant in a particular week
A few years ago, people tended to have relatively large CD collections. For students at a large university in the midwest, the mean number of CDs owned was 78 with a standard deviation of 90. To confirm these numbers, a random sample of 120 students from this university was collected and the size of their CD collections recorded. These particular 120 students had a mean CD collection size of 80 CDs.Select the correct description of the population mean in this study.
The mean number of CDs owned by all students at this university
At the Barilla plant in Ames, IA, a machine fills jars of marinara sauce with a population mean of 26.2 ounces of sauce and a population standard deviation of 0.04 ounces. To ensure the machine is operating properly, a quality assurance engineer randomly samples 34 jars out of all jars produced at the plant in the last week and finds the mean amount of sauce per jar is 26.197 ounces.What is the numerical value of the population mean?
26.2
At the Barilla plant in Ames, IA, a machine fills jars of marinara sauce with a population mean of 26.2 ounces of sauce and a population standard deviation of 0.04 ounces. To ensure the machine is operating properly, a quality assurance engineer randomly samples 34 jars out of all jars produced at the plant in the last week and finds the mean amount of sauce per jar is 26.197 ounces.Select the correct description of the sample in this study.
The 34 jars mentioned in the problem that were filled at the Barilla plan in Ames, IA during the last week and then selected and measured
The Foley Products Company has designed a new blend of concrete they believe will be twice as strong as their current high quality concrete. This new blend of concrete is believed to produce batches with a population mean strength of 15,000 psi and a population standard deviation of 2,000 psi. To validate this belief, they collect a random sample of 49 concrete batches out of all the batches produced at their plant in a particular week. The mean strength of the random sample of 49 concrete batches is measured to be 14,731 psi.Select the correct description of the sample in this study.
The 49 concrete batches of the new blend of concrete referred to in the problem
Diamond size is measured in carats. For ladies diamond rings, it is known the mean diamond size is 0.2 carats with a standard deviation of 0.057 carats. A company collected a random sample of 48 ladies diamond rings from all diamond companies and found these diamonds had a mean size of 0.204 carats.
Select the correct description of the sample mean in this study.
The mean diamond size of the 48 ladies diamond rings referred to in the problem
Diamond size is measured in carats. For ladies diamond rings, it is known the mean diamond size is 0.2 carats with a standard deviation of 0.057 carats. A company collected a random sample of 48 ladies diamond rings from all diamond companies and found these diamonds had a mean size of 0.204 carats.
What is the numerical value of the sample mean?
0.204
A few years ago, people tended to have relatively large CD collections. A random sample of 20 students from a large midwestern university was taken and the number of CDs for each student recorded in the table below.
79, 84, 83, 70, 89, 90, 82, 75, 92, 85
84, 63, 83, 66, 80, 76, 82, 72, 98, 77, 97
What is the sample mean number of CDs for these students?
81.25
At the Barilla plant in Ames, IA, a machine fills jars of marinara sauce with a population mean of 26.2 ounces of sauce and a population standard deviation of 0.04 ounces. To ensure the machine is operating properly, a quality assurance engineer randomly samples 34 jars out of all jars produced at the plant in the last week and finds the mean amount of sauce per jar is 26.197 ounces.Assume another employee randomly selects another 34 jars and weighs the sauce in each of these. The two sample means would most likely be different from each other due to sampling ___________________.
Variability
The Foley Products Company has designed a new blend of concrete they believe will be twice as strong as their current high quality concrete. This new blend of concrete is believed to produce batches with a population mean strength of 15,000 psi and a population standard deviation of 2,000 psi. To validate this belief, they collect a random sample of 49 concrete batches out of all the batches produced at their plant in a particular week. The mean strength of the random sample of 49 concrete batches is measured to be 14,731 psi.Match the description on the left with the correct distribution on the right.
A histogram of the strength of 49 batches of new blend concrete in the random sample: Sample Distribution
A histogram of the strength of all batches of the new blend concrete produced in their plant in a particular week. : Population Distribution
A histogram of the mean strength of all possible random samples of 49 batches of the new blend of concrete taken from this population: Sampling Distribution Model
A few years ago, people tended to have relatively large CD collections. For students at a large university in the midwest, the mean number of CDs owned was 78 with a standard deviation of 90. To confirm these numbers, a random sample of 120 students from this university was collected and the size of their CD collections recorded. These particular 120 students had a mean CD collection size of 80 CDs.What is the numerical value of the mean of the sampling distribution of the sample mean?
78
At the Barilla plant in Ames, IA, a machine fills jars of marinara sauce with a population mean of 26.2 ounces of sauce and a population standard deviation of 0.04 ounces. To ensure the machine is operating properly, a quality assurance engineer randomly samples 34 jars out of all jars produced at the plant in the last week and finds the mean amount of sauce per jar is 26.197 ounces.If the weight of all jars of sauce filled by the machine in the Barilla plant in Ames, IA follows a normal distribution, the shape of the sampling distribution of the sample mean follows a ___________ distribution.
Normal
The graphs below depict four distributions: the population distribution, and the sampling distribution of the sample mean for samples of size 10, 50, and 100.
The population sample is: The widest graph
The sampling distribution of the sample mean for samples of size 10: Second widest graph
The sampling distribution of the sample mean for samples of size 50 is: The second thinnest graph
The sampling distribution of the sample mean for samples of size 100 is: The thinnest graph
For which shape of a population distribution would you need the largest sample size to apply the Central Limit Theorem?
Heavily skewed distribution
A few years ago, people tended to have relatively large CD collections. For students at a large university in the midwest, the mean number of CDs owned was 78 with a standard deviation of 90. To confirm these numbers, a random sample of 120 students from this university was collected and the size of their CD collections recorded. These particular 120 students had a mean CD collection size of 80 CDs.If the distribution of the number of CDs was skewed to the right with a few large outliers, the shape of the sampling distribution of the sample mean
Is skewed to the right for smaller sample sizes but looks more like a normal distribution for larger sample sizes
The Foley Products Company has designed a new blend of concrete they believe will be twice as strong as their current high quality concrete. This new blend of concrete is believed to produce batches with a population mean strength of 15,000 psi and a population standard deviation of 2,000 psi. To validate this belief, they collect a random sample of 49 concrete batches out of all the batches produced at their plant in a particular week. The mean strength of the random sample of 49 concrete batches is measured to be 14,731 psi.Based on the histogram of the strength of the random sample of 49 concrete batches below and the description of the study, which of the necessary conditions for the sampling distribution of the sample mean to follow a normal model are satisfied?
10%, Randomization, and Nearly Normal Conditions
A few years ago, people tended to have relatively large CD collections. For students at a large university in the midwest, the mean number of CDs owned was 78 with a standard deviation of 90. To confirm these numbers, a random sample of 120 students from this university was collected and the size of their CD collections recorded. These particular 120 students had a mean CD collection size of 80 CDs.
Based on the histogram of the 120 CD collection sizes provided above and the description of the study, which of the necessary conditions for the sampling distribution of the sample mean to follow a normal model are satisfied?
10%, Randomization, and Nearly Normal Conditions
A few years ago, people tended to have relatively large CD collections. For students at a large university in the midwest (enrollment = 25,000), the mean number of CDs owned was 78 with a standard deviation of 90. To confirm these numbers, a random sample of 5,000 students from this university was collected and the size of their CD collections recorded. These particular 5,000 students had a mean CD collection size of 80 CDs.
Based on the histogram of the 5000 CD collection sizes provided above and the description of the study, which of the necessary conditions for the sampling distribution of the sample mean to follow a normal model is NOT satisfied in this study?
10% Condition
A few years ago, people tended to have relatively large CD collections. For students at a large university in the midwest (enrollment = 25,000), the mean number of CDs owned was 78 with a standard deviation of 90. To confirm these numbers, a random sample of 15 students from this university was collected and the size of their CD collections recorded. The mean number of CDs for this sample of students was 67.
Based on the histogram of the 15 CD collection sizes provided above and the description of the study, which of the necessary conditions for the sampling distribution of the sample mean to follow a normal model is NOT satisfied in this study?
Nearly Normal Conditions
At the Barilla plant in Ames, IA, a machine fills jars of marinara sauce with a population mean of 26.2 ounces of sauce and a population standard deviation of 0.04 ounces. To ensure the machine is operating properly a quality assurance engineer samples 34 jars of sauce by just selecting the first 34 jars he sees in a box.Based on the histogram and normal quantile plot provided and the description of the study, check which of the necessary conditions for the sampling distribution of the sample mean is NOT satisfied in this study?
Randomization Condition
A quantitative variable is recorded and used as numbers and has units
True
1. The group of all people you want to collect information from is called the ____
2. A numerical summary of information from the population is called a _____
3. A smaller group selected from the group we want to collect information is called a _____
4. A numerical summary of information from the sample is called a ____
1. Population
2. Parameter
3. Sample
4. Statistics
The mean and standard deviation are numerical summaries of ________ variables
Quantitative
Match the name to the correct symbol
a.) σ
b.) n
c.) ŷ
d.) μ
e.) s
Population Mean: D
Population Standard Deviation: A
Sample Mean: C
Sample Standard Deviation: E
Sample Size: B
The population distribution is the distribution of the quantitative variable in the population. This distribution is usually ___1____. The ___2___ is the distribution of the quantitative variable in the sample. This distribution is determined from the data in the ___3___ . The ___4___ is the distribution of all possible ___5___ calculated in repeated sampling from the population.
1. Population Distribution
2. Unknown
3. Sample Distribution
4. Sample
5. Sample Means
Shape:
Center:
Variability:
Shape: The Normal Model as long as the conditions hold
Center: The mean of sampling distribution is μ
Variability: The standard deviation of the sampling distribution
Sampling variability is the _______.
Variability expected between samples
The _____ requires that the sample be selected randomly from the population.
The _____ requires that the sample size be less than 10% of the population size.
The _____ requires the population distribution to be approximately a normal distribution for small sample sizes.
Randomization Condition
10% Condition
Nearly Normal Condition
For any non-normal population distribution, the Central Limit Theorem states the _______ will follow a normal distribution for all large sample sizes.
Sampling Distribution of the Sample Mean
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