Identify the Appropriate Statistical Technique to Use

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Identify the Appropriate Confidence Intervals and Hypothesis Tests

Hypothesis Tests for One Population Mean or Proportion

Hypothesis Test for a Population Proportion (1-Prop Z-Test):

This is used when the answer to the survey question is "Yes" or "No". That is used to see if a population proportion is less than, greater than, or not equal to some value, \(a\).

Null Hypothesis: The population proportion is equal to \(a. H_0: p = a\)

Alternative Hypothesis: The population proportion is less than, greater than, or not equal \(a. H_1: p < a, p > a, p \neq a\)

Use when you are given no list of data and no standard deviation.

Hypothesis Test for a Population Mean, Population Standard Deviation Given (z-Test):

This is used when the answer to the survey question is a number. That is used to see if a population mean is less than, greater than, or not equal to some value, \(a\).

Null Hypothesis: The population mean is equal to \(a. H_0: \mu = a\)

Alternative Hypothesis: The population mean is less than, greater than, or not equal \(a. H_1 \mu < a, \mu > a, \mu \neq a\)

Use whenever you are given a population standard deviation.

Hypothesis Test for a Population Mean, Population Standard Deviation Not Given (t-Test):

This is used when the answer to the survey question is a number. That is also used to see if a population mean is less than, greater than, or not equal to some value, \(a\).

Null Hypothesis: The population mean is equal to \(a. H_0 \mu = a\)

Alternative Hypothesis: The population mean is less than, greater than, or not equal \(a. H_1 \mu < a, \mu > a, \mu \neq a\)

Use whenever you are not given a population standard deviation.

Confidence Intervals for One Population Mean or Proportion

Confidence Interval for a Population Proportion (1-Prop Z-Int):

This is used when the answer to the survey question is "Yes" or "No". It is used to get an estimate for a range of values that the population proportion is likely to lie within.

Use when you are given no list of data and no standard deviation.

Hypothesis Test for a Population Mean, Population Standard Deviation Given (z-Test):

This is used when the answer to the survey question is a number. It is used to get an estimate for a range of values that the population mean is likely to lie within.

Use whenever you are given a population standard deviation.

Hypothesis Test for a Population Mean, Population Standard Deviation Not Given (t-Test):

This is used when the answer to the survey question is a number. It is used to get an estimate for a range of values that the population mean is likely to lie within.

Use whenever you are not given a population standard deviation.

Hypothesis Tests for Two Population Means or Proportions

Hypothesis Test for Comparing Two Population Proportions (2-Prop Z-Test):

This is used when the answer to the survey questions are "Yes" or "No". That is used to see if a population proportion is less than, greater than, or not equal to another population proportion.

Null Hypothesis: The population proportions are equal H_0: p_1 = p_2\)

Alternative Hypothesis: The first population proportion is less than, greater than, or not equal to the second. \(H_0: p_1 < p_2, p_1 > p_2, p_1 \neq p_2\)

Use when you are given no list of data and no standard deviation.

Hypothesis Test for Comparing Two Independent Population Means (2SampT-Test):

This is used when the answer to the survey question is a number. That is used to see if a population mean is less than, greater than, or not equal to a second population mean.

Null Hypothesis: The first population mean is equal to the second. \( H_0: \mu_1 = \mu_2\)

Alternative Hypothesis: The first population mean is less than, greater than, or not equal to the second. \(H_1: \mu_1< mu_2, \mu_1 > \mu_2, \mu_1 \neq \mu_2\)

Use when you are given two sample means and sample standard deviations, or two lists of data. The data sets must be independent.

Hypothesis Test for Comparing Two Dependent Population Means (PairedT-Test):

This is used when the answer to the survey question is a number. That is used to see if a population mean is less than, greater than, or not equal to a second population mean.

Null Hypothesis: The first population mean is equal to the second. \( H_0: \mu_d = 0\)

Alternative Hypothesis: The first population mean is less than, greater than, or not equal to the second. \(H_1: \mu_d< 0, \mu_d > 0, \mu_d \neq 0\)

Use when you are given two sample means and sample standard deviations, or two lists of data. The data sets must be dependent. Note: There will be the same sample sizes for the two samples.

Confidence Intervals for Two Population Means or Proportions

Confidence Interval for Comparing Two Population Proportions (2-Prop Z-Int):

This is used when the answer to the survey questions are "Yes" or "No". It is used to get an estimate for a range of values that the population proportion is likely to lie within.

Use when you are given no list of data and no standard deviation.

Confidence Interval Comparing Two Independent Population Means (2SampT-Test):

This is used when the answer to the survey question(s) is a number. It is used to get an estimate for a range of values that the difference in population means is likely to lie within.

Use when you are given two sample means and sample standard deviations, or two lists of data. The data sets must be independent.

Confidence Interval for Comparing Two Dependent Population Means (PairedT-Test):

This is used when the answer to the survey question(s) is a number. It is used to get an estimate for a range of values that the difference in the population means is likely to lie within.

Use when you are given two sample means and sample standard deviations, or two lists of data. The data sets must be dependent. Note: There will be the same sample sizes for the two samples.

Chi-Square Tests

Goodness of Fit Test

This is used when the answer to the survey question is qualitative (a word). It is used to decide if an unknown distribution fits a given known distribution, such as Normal, Uniform, or a known population distribution. You are given one observed distribution of counts and another listed of expected percents. If no percents are given and you want to see if the distribution is uniform (same percents in each category), then divide the total sample size by the number of categories. If percents are given, to get the expected counts multiply the percent converted to a decimal by the total sample size.

Null Hypothesis: The observed distribution is the same as the expected.

Alternative Hypothesis: The observed distribution is not the same as the expected.

Test for Homogeneity

This is used when there are two groups, each answering the same qualitative survey question that results in a word answer. It is used to decide if the distribution for the first group is the same as the distribution for the second group. Use when you are given two different sets of observed counts.

Null Hypothesis: The two distributions are the same.

Alternative Hypothesis: The two distributions are not the same.

Test for Independence

This is used when there are two quantitative survey questions that both result in a word answer. It is used to decide whether or not two categorical variables are related (dependent).

Null Hypothesis: The two variable are independent (not related).

Alternative Hypothesis: The two variable are dependent (related).

Test for Correlation

This is used when the answer to two survey questions are both quantitative (numbers). This is used to see if there is a correlation (linear relationship) between the two quantitative variables.

Null Hypothesis: There is no correlation between the two variables (\(H_0:\rho = 0\))

Alternative Hypothesis: There is a correlation between the two variables (\(H_1:\rho \neq 0\))

ANOVA

This is used when there are several quantitative (number answer) survey questions. It is used to see if at least two of the population means are different. It compares population means from three or more groups to see if any of them are different from each other. It is three or more lists of numbers instead of a table.

Null Hypothesis: All of the population means are the same. (\(H_0: \mu_1 = \mu_2 = ... = \mu_n\))

Alternative Hypothesis: At least two of the population means differ from each other.