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A population is the totality of all values (or measurements) of particular characteristics for a specified group of ______ that are of interest to the researcher.
A population is the totality of all values (or measurements) of particular characteristics for a specified group of ______ that are of interest to the researcher.
objects
Sampling is the process of choosing a ______ portion of a population.
Sampling is the process of choosing a ______ portion of a population.
representative
Due to limitations of time, money, personnel, it is impossible to study every ______ in the population.
Due to limitations of time, money, personnel, it is impossible to study every ______ in the population.
item
Probability sampling is when the selection of items is done according to some chance mechanism where elements have an equal chance of being ______.
Probability sampling is when the selection of items is done according to some chance mechanism where elements have an equal chance of being ______.
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In stratified random sampling, a population is divided into distinct subgroups, known as ______, based on shared characteristics.
In stratified random sampling, a population is divided into distinct subgroups, known as ______, based on shared characteristics.
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Cluster sampling consists of selecting clusters of ______ in a population and then obtaining a simple random sample of these clusters.
Cluster sampling consists of selecting clusters of ______ in a population and then obtaining a simple random sample of these clusters.
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A sample can be thoroughly studied due to its small ______.
A sample can be thoroughly studied due to its small ______.
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Fewer errors are encountered in the collection and handling of ______.
Fewer errors are encountered in the collection and handling of ______.
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Convenience sampling is a non-probability method where participants are selected based on their easy ______ and availability.
Convenience sampling is a non-probability method where participants are selected based on their easy ______ and availability.
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Multistage sampling involves selecting a sample in multiple stages, often by combining several ______ methods.
Multistage sampling involves selecting a sample in multiple stages, often by combining several ______ methods.
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______ statistics refers to methods for data collection, organization, classification, and summarization.
______ statistics refers to methods for data collection, organization, classification, and summarization.
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Inferential statistics helps in drawing a conclusion about a population based on information obtained from a ______.
Inferential statistics helps in drawing a conclusion about a population based on information obtained from a ______.
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Parameters are numbers that describe the characteristics of a ______.
Parameters are numbers that describe the characteristics of a ______.
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A ______ is a number that describes the characteristics of a sample.
A ______ is a number that describes the characteristics of a sample.
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The process of data ______, classification, organization, and interpretation is a key component of statistics.
The process of data ______, classification, organization, and interpretation is a key component of statistics.
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Measures of ______ tendency and variability are part of descriptive statistics calculations.
Measures of ______ tendency and variability are part of descriptive statistics calculations.
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A ______ is a prediction based on a body of knowledge, scientific theory, or observations.
A ______ is a prediction based on a body of knowledge, scientific theory, or observations.
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The ______ hypothesis (Ho) indicates the value of the population parameter to be tested.
The ______ hypothesis (Ho) indicates the value of the population parameter to be tested.
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The ______ hypothesis (Ha) is the operational statement of the experimenter's research hypothesis.
The ______ hypothesis (Ha) is the operational statement of the experimenter's research hypothesis.
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In stating the level of significance (α), the researcher sets up the rejection region and ______ region for the null hypothesis.
In stating the level of significance (α), the researcher sets up the rejection region and ______ region for the null hypothesis.
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The rejection region is called the ______ region.
The rejection region is called the ______ region.
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Use the Z-test when ______ > 30 to compare the mean of a particular sample to the mean of the population.
Use the Z-test when ______ > 30 to compare the mean of a particular sample to the mean of the population.
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The claim of the Liwanag Bulb Company is that it sells light bulbs with an average life of ______ hours.
The claim of the Liwanag Bulb Company is that it sells light bulbs with an average life of ______ hours.
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A sample of 64 new bulbs had an average lifetime of ______ hours.
A sample of 64 new bulbs had an average lifetime of ______ hours.
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The claimed population mean (μ) for the first test is ______ hours.
The claimed population mean (μ) for the first test is ______ hours.
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The sample mean (xˉ) found in the first hypothesis test is ______ hours.
The sample mean (xˉ) found in the first hypothesis test is ______ hours.
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The sample size (N) used in the hypothesis tests is ______.
The sample size (N) used in the hypothesis tests is ______.
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The significance level (α) set for the tests is ______.
The significance level (α) set for the tests is ______.
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To decide on the claim about the mixed nuts, a sample of ______ cans was used.
To decide on the claim about the mixed nuts, a sample of ______ cans was used.
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For the cashew nut test, the average found was ______ cashew nuts per can.
For the cashew nut test, the average found was ______ cashew nuts per can.
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The sample standard deviation (s) in the nut test was ______ cashew nuts.
The sample standard deviation (s) in the nut test was ______ cashew nuts.
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A T-test should be used when the sample size is considered ______.
A T-test should be used when the sample size is considered ______.
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The dissolved oxygen readings in parts per million (ppm) are recorded as follows: Above town: 4.9, 5.2, 5.1, 4.8, ______
The dissolved oxygen readings in parts per million (ppm) are recorded as follows: Above town: 4.9, 5.2, 5.1, 4.8, ______
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The test statistic in ANOVA is known as the ______, which is the ratio of the variance between groups to the variance within groups.
The test statistic in ANOVA is known as the ______, which is the ratio of the variance between groups to the variance within groups.
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A higher F-value suggests that the group means are significantly ______.
A higher F-value suggests that the group means are significantly ______.
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The Analysis of Variance (ANOVA) is used to compare ______ or more sample means.
The Analysis of Variance (ANOVA) is used to compare ______ or more sample means.
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Groups of students were randomly assigned to be taught using four different ______ techniques.
Groups of students were randomly assigned to be taught using four different ______ techniques.
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The number of students varied from group to group due to ______ in the experimental groups.
The number of students varied from group to group due to ______ in the experimental groups.
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The hypothesis test being discussed is concerned with comparing means from ______ sample groups.
The hypothesis test being discussed is concerned with comparing means from ______ sample groups.
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To determine if the data presents sufficient evidence of a difference in the mean achievement, a statistical ______ is conducted.
To determine if the data presents sufficient evidence of a difference in the mean achievement, a statistical ______ is conducted.
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Study Notes
Sampling
- A population is the totality of all values (or measurements) of specific characteristics for a group of interest to a researcher.
- A sample is a limited portion of a population used in a study.
- Sampling is the process of selecting a representative subset of a population.
Reasons for Sampling
- Time, money, and personnel limitations make studying every item in a population impossible.
- Examining an item may require destroying it.
- Small samples can be thoroughly studied.
- Fewer errors occur during data collection and handling.
- Studying larger or diverse populations is more cost-effective.
Types of Samples
- Probability samples involve selecting items based on a chance mechanism where each item has an equal chance of selection.
- Non-probability samples involve selecting items based on judgment where items don't have an equal chance of being selected.
Sampling Methods
- Simple Random Sampling: A process of selecting a sample from a population where every unit has an equal chance of inclusion. An example is lottery sampling.
- Stratified Random Sampling: A method where a population is divided into subgroups (strata) based on shared characteristics, and a random sample is drawn from each stratum.
- Cluster Sampling: A method where clusters of units are selected from a population, and a simple random sample of these clusters is drawn. This is cost-effective for large, geographically dispersed populations.
- Convenience Sampling: A non-probability method where participants are selected based on accessibility and availability to the researcher.
Statistics
- Statistics deals with experimental designs, data collection, classification, organization, interpretation, and decision-making based on data.
- Descriptive statistics: Methods of data collection, organization, classification, summarization, and presentation (e.g., graphs, tables, charts). Includes calculating central tendency (mean, median, mode) and measures of variability (range, standard deviation, variance).
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Inferential statistics: Arriving at conclusions about a population based on information from a sample.
- Parameters: Numerical values describing population characteristics.
- Statistics: Numerical values describing sample characteristics.
Hypothesis
- A prediction based on knowledge, scientific theory, or observations.
- Null hypothesis (H₀): The value of a population parameter to be tested.
- Alternative hypothesis (H₁): The researcher's research hypothesis.
Level of Significance and Sample Size
- The level of significance (α) sets up a rejection region (critical region) and an acceptance region for a null hypothesis.
One Sample Hypothesis Test of Means
-
Z-test: Used when the sample size (N) is greater than 30 to compare sample mean to population mean.
- Z = (x̄ - μ) / (σ/√n)
- Where: x̄ = Sample mean, μ = Population mean, σ = Population standard deviation, n = Sample size
- T-test: Used when the sample size (N) is less than or equal to 30. - t = (x̄ - μ) / (s/√n) - Where: x̄ = Sample mean, μ = Population mean, s = Sample standard deviation, n = Sample size
Two Sample Hypothesis Test of Means
- Used to compare the means of two independent groups.
- Equal Variance (Pooled T-test): Assumes the variances of the groups are equal.
- Unequal Variance (Welch's T-test): Assumes variances are different.
Three or More Sample Hypothesis Test of Means (ANOVA)
- Analysis of Variance (ANOVA): Used to compare three or more sample means.
- F-statistic: The test statistic in ANOVA, calculated as the ratio of variance between groups to variance within groups. A higher F-value suggests significant differences among group means.
- Formula: F = MSB / MSW - Where: MSB = Mean Square Between, MSW = Mean Square Within.
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Description
Test your understanding of key concepts related to sampling methods in statistics. This quiz covers the definitions and processes associated with populations, sampling techniques, and potential errors. Ideal for students looking to reinforce their knowledge of statistical sampling concepts.
