Statistics: Null and Alternative Hypotheses

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Questions and Answers

Which of the following statements accurately describes the null hypothesis?

  • It is always the hypothesis that is assumed to be true. (correct)
  • It is always the hypothesis that is rejected.
  • It is always the hypothesis that contains an equality statement. (correct)
  • It is always the hypothesis that is being tested.

In a non-directional hypothesis test, what is the alternative hypothesis?

  • The population parameter is less than a specified value.
  • The population parameter is not equal to a specified value. (correct)
  • The population parameter is greater than a specified value.
  • The population parameter is equal to a specified value.

What is the level of significance in hypothesis testing?

  • The probability of rejecting a true null hypothesis. (correct)
  • The probability of rejecting a false null hypothesis.
  • The probability of accepting a false null hypothesis.
  • The probability of accepting a true null hypothesis.

A researcher wants to test if the mean height of women in a city is different from 5'4". What type of hypothesis test should they use?

<p>Two-tailed test (B)</p>
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A company claims that their new fertilizer increases the mean yield of tomatoes. A farmer wants to see if this claim is true. What type of hypothesis test should the farmer use?

<p>Right-tailed test (A)</p>
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If a hypothesis test has a level of significance of 0.01, what is the probability of rejecting a true null hypothesis?

<p>0.01 (D)</p>
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A researcher wants to test if the mean weight of newborn babies in a hospital is less than 7 pounds. What type of hypothesis test should they use?

<p>Left-tailed test (D)</p>
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A study is conducted to see if there is a significant difference in the average number of hours students spend studying per week between those who use social media daily and those who do not. What type of hypothesis test should be used?

<p>Two-tailed test (C)</p>
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What is the null hypothesis when a professor wants to show that the mean score of Method A is higher than Method B?

<p>The mean score in Method A is not higher than that of Method B. (C)</p>
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Which statement describes the alternative hypothesis regarding the coffee shop's customer count?

<p>Fewer than 500 customers visit the shop daily. (B)</p>
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What is the alternative hypothesis in testing math anxiety cases between females and males?

<p>There is a significant difference between male and female math anxiety cases. (C)</p>
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In the context of the psychologist's hypothesis about soft music during a Statistics test, what is the null hypothesis?

<p>Playing soft music does not affect average scores. (A)</p>
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What is the goal of the teacher wishing to determine if there's a significant difference in test scores between morning and afternoon classes?

<p>To find out if there is no difference in scores between the classes. (C)</p>
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When a mathematics teacher aims to show that male students outperform female students, what is the null hypothesis?

<p>There is no difference in performance between male and female students. (C)</p>
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Which of the following hypotheses is implied when a researcher investigates the average score difference across various teaching methods?

<p>Some teaching methods lead to better scores than others. (B)</p>
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What can be considered the null hypothesis for a scenario where a person believes that a new policy will not change customer traffic?

<p>The new policy will have no effect on customer traffic. (D)</p>
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What is the primary goal of research and statistics according to the content?

<p>Decision-making (A)</p>
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Which step comes first in the hypothesis testing process?

<p>Formulate the null and alternative hypotheses (B)</p>
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Which of the following correctly represents a null hypothesis?

<p>The average life expectancy of females is not different from that of males. (C)</p>
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What does the alternative hypothesis represent?

<p>The possibility of a statistically significant effect. (D)</p>
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In hypothesis testing, the rejection region is defined during which step?

<p>Determining the level of significance (D)</p>
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How is a statistical hypothesis defined?

<p>A statement about a population parameter. (B)</p>
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What type of test is used when the hypotheses are based on directional claims?

<p>Right-tailed test (A)</p>
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What is an example of a left-tailed hypothesis test?

<p>The average score of students is less than 75. (B)</p>
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What characterizes a directional test of hypothesis?

<p>It focuses on one side of the distribution. (D)</p>
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Which of the following best describes a right-tailed test?

<p>It is concerned with the positive end of the distribution. (A)</p>
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In a left-tailed test, what is the nature of the alternative hypothesis?

<p>It suggests the parameter is less than a certain value. (C)</p>
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Which of the following statements is true about two-tailed tests?

<p>They are used when no assertion about the parameter's direction is made. (A)</p>
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When formulating hypotheses, what do the null and alternative hypotheses represent in a one-tailed test?

<p>The null hypothesizes no difference, while the alternative predicts a specific direction. (B)</p>
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What is the typical use of the phrase 'not equal to' in hypothesis testing?

<p>It is characteristic of a two-tailed test. (C)</p>
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What distinguishes a hypothesis test from a mere assertion?

<p>A hypothesis test requires empirical evidence. (A)</p>
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In hypothesis testing, what role does the null hypothesis serve?

<p>It provides a benchmark for comparison. (D)</p>
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What is the null hypothesis for the mean frequency of exercise between young and old people?

<p>The mean frequency of exercise is the same for young and old people. (C)</p>
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In the case of the clothing shop, what is the alternative hypothesis?

<p>The daily mean number of customers is greater than 246. (B)</p>
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Which statement correctly represents the null and alternative hypotheses for the college professor’s programming test scenario?

<p>The mean score using Method A is equal to the mean score using Method B; the mean score using Method A is higher than Method B. (B)</p>
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Which hypothesis would you state if a researcher wants to examine if there is no difference in exercise frequency between two age groups?

<p>The average exercise frequency for young and old people is the same. (B)</p>
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For the clothing shop’s hypothesis testing, which of the following statements could be considered a misconception about the null hypothesis?

<p>The null hypothesis can be stated as there are no customers. (A)</p>
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What is the purpose of stating alternative hypotheses in research?

<p>To indicate the potential direction or relationship being tested. (C)</p>
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Why is it important to differentiate between young and old people when studying exercise frequency?

<p>Different age groups may have different health needs and activity levels. (D)</p>
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Which of the following statements represents the null hypothesis best in the context of customer counts in the clothing shop?

<p>The average daily number of customers is not greater than 246. (A)</p>
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Flashcards

Hypothesis Testing

A statistical method to assess if a hypothesis about a population is true using sample data.

Null Hypothesis

The hypothesis assumed to be true, often stating no effect or relationship, denoted H₀.

Alternative Hypothesis

The hypothesis contrary to the null, indicating an effect or relationship, denoted H₁.

Right-Tailed Test

A hypothesis test where the rejection region is in the right tail of the distribution.

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Left-Tailed Test

A hypothesis test where the rejection region is in the left tail of the distribution.

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Two-Tailed Test

A hypothesis test where the rejection regions are in both tails of the distribution.

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Level of Significance

The probability threshold at which the null hypothesis is rejected, often denoted by alpha (α).

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Test Statistic

A standardized value that is calculated from sample data during a hypothesis test, used to compare against a critical value.

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Directional Test of Hypothesis

A hypothesis test that uses only one tail of the distribution, either right or left.

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Null Hypothesis (Right-tailed)

Assumes the parameter is less than or equal to a specified value in a right-tailed test.

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Null Hypothesis (Left-tailed)

Assumes the parameter is not less than a specified value in a left-tailed test.

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Non-directional Test of Hypothesis

A two-tailed hypothesis test that tests for any difference, not specifying a direction.

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Alternative Hypothesis (Two-tailed)

In a two-tailed test, it states the parameter is not equal to a specific value.

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Comparative Terms in Hypotheses

Words like greater than, less than, not equal to used in expressing hypotheses.

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Non-directional Test

A test to determine if a parameter differs from a value without a specified direction.

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Null Hypothesis (H0)

The assertion that there is no effect or difference, used as a starting point in hypothesis testing.

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Alternative Hypothesis (H1)

The hypothesis that proposes a change or difference, opposing the null hypothesis.

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Significance Level Example

A level set to control the likelihood of incorrectly rejecting a true null hypothesis, like 5%.

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Mean Score Method A

The average score of students taught using Method A.

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Mean Score Method B

The average score of students taught using Method B.

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Null Hypothesis Example

The mean score in Method A is not higher than Method B (H₀).

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Alternative Hypothesis Example

The mean score in Method A is higher than Method B (H₁).

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Coffee Shop Hypothesis

Test if customer visits decrease after competitor opens.

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Gender Math Anxiety Hypothesis

Investigates mean differences in math anxiety between genders.

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Soft Music Test Hypothesis

Tests if soft music improves statistics scores.

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Morning vs Afternoon Classes Hypothesis

Tests if there's a significant score difference between class times.

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Null Hypothesis Example (Exercise)

There is no significant difference in exercise frequency between young and old people.

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Alternative Hypothesis Example (Exercise)

There is a significant difference in exercise frequency between young and old people.

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Null Hypothesis Example (Customers)

The daily mean number of customers is less than or equal to 246.

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Alternative Hypothesis Example (Customers)

The daily mean number of customers is greater than 246.

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Null Hypothesis Example (Scores)

The mean score of Method A is less than or equal to that of Method B.

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Alternative Hypothesis Example (Scores)

The mean score of Method A is higher than that of Method B.

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Mean Frequency of Exercise

The average amount of exercise performed by a population group.

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Daily Average Customers

The mean number of customers visiting a store daily.

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Study Notes

Null and Alternative Hypotheses

  • Hypothesis testing is a statistical method used to assess the probability of a given hypothesis about a population being true, using sample data.
  • The null hypothesis, denoted by , is the hypothesis assumed to be true. It often includes a statement of equality (e.g., "is equal to," "is less than or equal to," "is greater than or equal to").
  • The alternative hypothesis, denoted by , is the hypothesis contrary to the null hypothesis. It does not include a statement of equality (e.g., "is not equal to," "is less than", "is greater than").
  • The level of significance is the probability of rejecting a true null hypothesis; it's denoted by . Common levels are 0.05 (5%) and 0.01 (1%).
  • Hypothesis testing involves steps: formulating the null and alternative hypotheses, establishing a significance level, calculating test statistics, determining a rejection region, making a decision, and drawing a conclusion.
  • Different types of tests exist:
    • One-tailed (directional): used if the hypothesis involves a specific direction (e.g., greater than or less than).
      • Right-tailed: parameter falls within the positive end of the distribution. The alternative hypothesis uses comparatives (e.g., greater than, higher than).
      • Left-tailed: parameter falls within the negative end of the distribution. The alternative hypothesis uses comparatives (e.g., less than, lower than).
    • Two-tailed (non-directional): used when no specific direction is proposed. The alternative hypothesis uses comparatives that do not imply a direction (e.g., not equal to, different from).

Activity Examples

  • Example 1 (Exercise Frequency): A researcher wants to know if there's a significant difference in the mean frequency of exercise between young and old people.

    • Null Hypothesis: There is no significant difference in mean exercise frequency between young and old people.
    • Alternative Hypothesis: There is a significant difference in mean exercise frequency between young and old people.

  • Example 2 (Clothing Shop Customers): A store owner wants to know if the daily average number of customers is greater than 246.

    • Null Hypothesis: The daily mean number of customers is less than or equal to 246.
    • Alternative Hypothesis: The daily mean number of customers is greater than 246.

  • Example 3 (Programming Test Scores): A college professor wants to show that the mean score in a programming test for students taught using Method A is higher than the mean score for students taught using Method B.

    • Null Hypothesis: The mean score in the programming test for students taught using Method A is not higher than that for students taught using Method B.
    • Alternative Hypothesis: The mean score in the programming test for students taught using Method A is higher than that for students taught using Method B.

  • Activity 2 (More Examples): Several other examples, like a coffee shop owner wanting to see if daily customer numbers are decreasing, determining if there are differences in math anxiety between genders, checking if music improves test scores, and analyzing differences in student scores between classes. The examples are intended for developing hypotheses, not solutions.

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