Session 3 Statistical inference
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Questions and Answers

What does the null hypothesis in the two-sample barista example assume?

  • The true average amount poured is greater than twelve ounces.
  • The two baristas pour the same amount of coffee on average. (correct)
  • The two baristas pour different amounts of coffee on average.
  • The average amount poured by the two baristas is equal to twelve ounces.

    • In hypothesis testing, what is the purpose of the alternative hypothesis?

  • To show that there is a difference in population parameters. (correct)
  • To always reject the null hypothesis.
  • To prove the null hypothesis true.
  • To provide a specific value for comparison.

    • What is a two-sided test primarily used for?

  • Testing if the average amount is exactly twelve ounces.
  • Testing if one population parameter is less than a specific value.
  • Testing if the population parameter is not equal to a specified value. (correct)
  • Testing if two population parameters are equal.

    • What does a right-sided hypothesis test indicate?

    <p>The population parameter is greater than the null hypothesis value.</p> Signup and view all the answers

    In the scenario where the home barista is compared to the work barista, what would a left-sided test suggest?

    <p>The home barista pours more than the work barista.</p> Signup and view all the answers

    When gathering evidence for hypothesis testing, what initial assumption is made?

    <p>The null hypothesis is true.</p> Signup and view all the answers

    If one wants to test if the true average amount poured is not equal to twelve ounces, what kind of test should be used?

    <p>A two-sided test.</p> Signup and view all the answers

    In the two-sample case, what would a two-sided alternative hypothesis state?

    <p>The two population parameters are not equal.</p> Signup and view all the answers

    What type of employer is represented by the number 1 in the Employer variable?

    <p>Government</p> Signup and view all the answers

    How is the Income variable defined in the GSS data?

    <p>Yearly income from primary job</p> Signup and view all the answers

    What does the variable 'Years Employed' indicate in the GSS dataset?

    <p>Years with the current employer</p> Signup and view all the answers

    In the recent GSS dataset, what is the typical frequency of the surveys conducted?

    <p>Every other year</p> Signup and view all the answers

    Which variable in the GSS dataset provides a unique identifier for each entry?

    <p>Id</p> Signup and view all the answers

    What is the maximum number of hours worked per week according to the provided data?

    <p>56 hours</p> Signup and view all the answers

    Which of the following years of employment is associated with the highest income in the GSS data sample?

    <p>7 years</p> Signup and view all the answers

    Which statement about the GSS data regarding employment is true?

    <p>The data measures various variables across different employer types.</p> Signup and view all the answers

    What is the purpose of calculating a confidence interval for the sample estimate of p?

    <p>To understand the range of plausible values for the population proportion.</p> Signup and view all the answers

    What does the term 𝑝̂ represent in the confidence interval formula?

    <p>The sample estimate of the population proportion.</p> Signup and view all the answers

    In the confidence interval formula, what does the symbol 𝑧 ∗ signify?

    <p>A constant representing the desired level of confidence.</p> Signup and view all the answers

    When calculating a 95% confidence interval, what value is typically used for 𝑧 ∗?

    <p>1.96</p> Signup and view all the answers

    What is the interpretation of the confidence interval [0.2124, 0.3998]?

    <p>We are 95% confident the true population proportion is between 21.24% and 39.98%.</p> Signup and view all the answers

    How would adjusting the value of 𝑧 ∗ affect the width of the confidence interval?

    <p>It would widen the confidence interval.</p> Signup and view all the answers

    What is the significance of the sample size 'n' in the confidence interval formula?

    <p>It impacts the variance of the estimate.</p> Signup and view all the answers

    Which of the following is NOT true regarding the confidence interval calculated in this context?

    <p>The sample estimate can be viewed as the true population proportion.</p> Signup and view all the answers

    What is the null hypothesis (H0) in the two-sample t-test scenario described?

    <p>There is no difference in the average employment duration between government and private sector workers.</p> Signup and view all the answers

    What does the alternative hypothesis (Ha) indicate in this hypothesis test?

    <p>There is a difference in the average employment duration between government workers and private sector workers.</p> Signup and view all the answers

    What is the significance of the p-value obtained in the two-sample t-test?

    <p>A small p-value suggests strong evidence against the null hypothesis.</p> Signup and view all the answers

    In the described two-sample t-test, what is the significance of the average years employed (x̅) for government and private sector workers?

    <p>It provides estimates to compare employment duration between the groups.</p> Signup and view all the answers

    What conclusion can be drawn from the small p-value (0.0002462) in the context of the two-sample t-test?

    <p>There is strong evidence to reject the null hypothesis.</p> Signup and view all the answers

    What mathematical notation is used to express the null hypothesis for this hypothesis test?

    <p>μ1 = μ2</p> Signup and view all the answers

    Which of the following statements is true about the two-sample t-test being conducted?

    <p>It compares the average years employed between two distinct groups.</p> Signup and view all the answers

    What sample means are being compared in this two-sample t-test?

    <p>The average years employed of government workers (11.11) and private sector workers (7.90).</p> Signup and view all the answers

    What is the null hypothesis (H0) for comparing the earnings of government and private sector workers?

    <p>On average, government workers earn the same as private sector workers.</p> Signup and view all the answers

    What does a p-value of 0.06765 indicate in relation to the threshold of 0.05?

    <p>Insufficient evidence to reject the null hypothesis.</p> Signup and view all the answers

    In a right-sided test, what does the alternative hypothesis (Ha) signify?

    <p>The mean of group 1 is greater than the mean of group 2.</p> Signup and view all the answers

    What does the notation µ1 − µ2 > 0 represent?

    <p>Government workers earn more than private sector workers.</p> Signup and view all the answers

    What average income is reported for private-sector employees in the sample?

    <p>$40,847.81</p> Signup and view all the answers

    If the p-value is below the threshold of 0.05, what action would be appropriate?

    <p>Reject the null hypothesis.</p> Signup and view all the answers

    What key information is provided by the average incomes of government and private-sector workers?

    <p>It allows comparison between the average incomes of both groups.</p> Signup and view all the answers

    What is the null hypothesis when comparing two population proportions?

    <p>𝐻𝑜 : 𝑝1 = 𝑝2</p> Signup and view all the answers

    Which of the following represents a left-sided alternative hypothesis?

    <p>𝐻𝑎 : 𝑝1 − 𝑝2 &lt; 0</p> Signup and view all the answers

    In the example given, how many students were surveyed who had Professor Bojinov?

    <p>75</p> Signup and view all the answers

    What alternative hypothesis signifies no difference in proportions?

    <p>𝐻𝑎 : 𝑝1 − 𝑝2 = 0</p> Signup and view all the answers

    What is the correct alternative hypothesis for showing a significant difference in proportions?

    <p>𝐻𝑎 : 𝑝1 − 𝑝2 ≠ 0</p> Signup and view all the answers

    If a significant difference is found in the proportions of satisfied students, which hypothesis is rejected?

    <p>𝐻𝑜 : 𝑝1 = 𝑝2</p> Signup and view all the answers

    How many students reported satisfaction with Professor Parzen?

    <p>48</p> Signup and view all the answers

    Which aspect is NOT part of conducting a two-sample test of proportions?

    <p>Determining sample size</p> Signup and view all the answers

    Study Notes

    Statistical Inference

    • Statistics are used to make better business decisions by analyzing data and modeling uncertainty.
    • A population is the entire collection of individuals, objects, or things being studied.
    • A sample is a randomly selected subset of the population used to draw conclusions about the population.
    • Confidence intervals are used to estimate population quantities based on sample data.
    • Hypothesis testing is used to evaluate the validity of specific hypotheses about a population.
    • Sampling is a crucial technique to efficiently acquire data, as studying entire populations is often impractical.

    Samples and Populations

    • Populations are the entire set of individuals, things, or objects of interest.
    • Samples are subsets of the population, used to gather data about the population.
    • Statistics are numerical properties of samples, such as means, proportions, and variances.
    • These statistics are used to estimate parameters (properties of the population).

    Confidence Intervals

    • Confidence intervals provide a range of plausible values for a population parameter based on sample data.
    • The variability in sample statistics due to random sampling is accounted for in confidence intervals.
    • Confidence intervals can be created for various parameters like proportions and means.

    Confidence Intervals for Proportions

    • Confidence intervals for proportions use sample data (proportion) to estimate the true population proportion.
    • The formula involves the sample proportion, the z-score (related to the desired confidence level), and the sample size.
    • Z score values are associated with different confidence levels (90%, 95%, etc.). Higher confidence levels result in wider intervals.

    Confidence Intervals for Means

    • Confidence intervals for means use sample data (mean and standard deviation) to estimate the true population mean.
    • The formula involves the sample mean, the t-score (related to the desired confidence level and degrees of freedom), the sample standard deviation, and the sample size.
    • The t-score value depends on confidence level and degrees of freedom. These are related to sample size and need to be calculated from a table or using statistical software like R.

    Hypothesis Testing

    • Hypothesis testing analyzes sample data to evaluate claims (hypotheses) about a population.
    • The process involves setting up null and alternative hypotheses. The null hypothesis (Ho) states a claim about a population parameter. The alternative hypothesis (Ha) is the potential alternative.
    • Sample data is used to evaluate evidence supporting a hypothesis related to a characteristic of the population.

    One-Sample Hypothesis Testing

    • One-sample tests are used to compare a single population parameter (like mean or proportion) to a specific value.
    • Common scenarios include verifying if a population mean is equal to a particular value, or if a population parameter is within a specified range.

    Two-Sample Hypothesis Testing

    • Two-sample tests compare parameters for two independent populations.
    • Appropriate tests are used based on whether testing means or proportions, and if the tests are one-sided or two-sided.
    • Tests can compare differences (or equality) in means or proportions.

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    Statistical Inference PDF

    Description

    This quiz focuses on key concepts in hypothesis testing, including the null and alternative hypotheses, types of tests, and the implications of various statistical tests. It explores scenarios involving barista comparisons and the interpretation of variables from the GSS dataset. Test your understanding of these statistical principles!

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