Podcast
Questions and Answers
Why is hypothesis testing considered a crucial process in statistics?
Why is hypothesis testing considered a crucial process in statistics?
- It helps in presenting data visually through graphs.
- It validates assumptions about a population using experimental data. (correct)
- It simplifies complex mathematical equations.
- It ensures all statistical calculations are error-free.
A researcher is evaluating the effectiveness of a new drug. What is the primary role of formulating a null hypothesis in this scenario?
A researcher is evaluating the effectiveness of a new drug. What is the primary role of formulating a null hypothesis in this scenario?
- To define the range of acceptable dosages for the drug.
- To predict the expected improvement in patients' health.
- To assume the drug has no effect, providing a baseline for comparison. (correct)
- To determine the cost-effectiveness of the drug compared to existing treatments.
In hypothesis testing, what is the purpose of the alternative hypothesis?
In hypothesis testing, what is the purpose of the alternative hypothesis?
- To state there is no difference between parameters.
- To establish a baseline for statistical insignificance.
- To act as the opposite or negation of the null hypothesis. (correct)
- To ensure the sample data perfectly matches the population.
When formulating a null hypothesis ($H_0$), which of the following conditions should be present?
When formulating a null hypothesis ($H_0$), which of the following conditions should be present?
A researcher claims that the average height of Grade 12 students is significantly higher than 66 inches. What would be the appropriate null hypothesis ($H_0$) to test this claim?
A researcher claims that the average height of Grade 12 students is significantly higher than 66 inches. What would be the appropriate null hypothesis ($H_0$) to test this claim?
A study aims to verify if the average monthly income of families in a low-income bracket is $7,500. If (\mu) represents the average monthly income, which of the following is the correct way to express the alternative hypothesis ($H_a$)?
A study aims to verify if the average monthly income of families in a low-income bracket is $7,500. If (\mu) represents the average monthly income, which of the following is the correct way to express the alternative hypothesis ($H_a$)?
A company asserts that no more than 60% of registered voters support a local election candidate. What is the appropriate alternative hypothesis ($H_a$)?
A company asserts that no more than 60% of registered voters support a local election candidate. What is the appropriate alternative hypothesis ($H_a$)?
What does the level of significance ($\alpha$) in hypothesis testing represent?
What does the level of significance ($\alpha$) in hypothesis testing represent?
If a researcher sets the level of significance ($\alpha$) at 0.05, what does this imply regarding the hypothesis testing?
If a researcher sets the level of significance ($\alpha$) at 0.05, what does this imply regarding the hypothesis testing?
In a hypothesis test, what is the core distinction between a one-tailed test and a two-tailed test?
In a hypothesis test, what is the core distinction between a one-tailed test and a two-tailed test?
A registrar believes that the average number of enrollees this school year is not the same as last year. What type of hypothesis test is most appropriate?
A registrar believes that the average number of enrollees this school year is not the same as last year. What type of hypothesis test is most appropriate?
Under what circumstances is a left-tailed test most suitable for hypothesis testing?
Under what circumstances is a left-tailed test most suitable for hypothesis testing?
What is the primary role of the 'rejection region' in hypothesis testing?
What is the primary role of the 'rejection region' in hypothesis testing?
What does the 'critical value' represent in the context of hypothesis testing?
What does the 'critical value' represent in the context of hypothesis testing?
What is the decision rule when the computed test statistic falls within the non-rejection region?
What is the decision rule when the computed test statistic falls within the non-rejection region?
What is a Type I error in hypothesis testing?
What is a Type I error in hypothesis testing?
How is a Type II error defined in the context of hypothesis testing?
How is a Type II error defined in the context of hypothesis testing?
In a clinical trial, a new medicine is tested for its effectiveness. Which statement illustrates a Type I error?
In a clinical trial, a new medicine is tested for its effectiveness. Which statement illustrates a Type I error?
In the context of starting a food cart business, what would be the consequence of a Type II error?
In the context of starting a food cart business, what would be the consequence of a Type II error?
In daily water quality testing, what is the risk related to Type II error?
In daily water quality testing, what is the risk related to Type II error?
When the null hypothesis is true, failing to reject it results in which type of decision?
When the null hypothesis is true, failing to reject it results in which type of decision?
If a null hypothesis is false and a researcher rejects it, what type of decision is made?
If a null hypothesis is false and a researcher rejects it, what type of decision is made?
In hypothesis testing, how does increasing the sample size generally affect the likelihood of Type II error, assuming other factors are constant?
In hypothesis testing, how does increasing the sample size generally affect the likelihood of Type II error, assuming other factors are constant?
A researcher is testing a hypothesis with a level of significance ($\alpha$) of 0.01. What impact does reducing the level of significance have on Type I error?
A researcher is testing a hypothesis with a level of significance ($\alpha$) of 0.01. What impact does reducing the level of significance have on Type I error?
A computed t-value is at the non-rejection region. What decision must be made?
A computed t-value is at the non-rejection region. What decision must be made?
The computed z-value is at the rejection region. What decision must be made?
The computed z-value is at the rejection region. What decision must be made?
What is the critical value if two-tailed test at 5% level of significance is performed?
What is the critical value if two-tailed test at 5% level of significance is performed?
Sofia computed for the t-value using a formula given the following values. Mean is 142, standard deviation is 19.855, the standard population is 152, and a sample size of 10. Which of the following is the computed t-value?
Sofia computed for the t-value using a formula given the following values. Mean is 142, standard deviation is 19.855, the standard population is 152, and a sample size of 10. Which of the following is the computed t-value?
What does a null hypothesis state?
What does a null hypothesis state?
Alternative hypothesis is considered the ________ of the null hypothesis?
Alternative hypothesis is considered the ________ of the null hypothesis?
A significance level measures the probability of?
A significance level measures the probability of?
If the alternative hypothesis uses "$
eq$" for the population mean, the statistical test is:
If the alternative hypothesis uses "$ eq$" for the population mean, the statistical test is:
What can be referred to as the set of values for the test statistic that causes us to the reject the null hypothesis?
What can be referred to as the set of values for the test statistic that causes us to the reject the null hypothesis?
How can a Type II error can be reduced?
How can a Type II error can be reduced?
Why are critical values of test statistics used?
Why are critical values of test statistics used?
If Sofia rejects her null hypothesis even when it turns out to be true, what has she committed?
If Sofia rejects her null hypothesis even when it turns out to be true, what has she committed?
What would result to a conclusion if a null hypothesis is false but fails to reject it?
What would result to a conclusion if a null hypothesis is false but fails to reject it?
A teacher formulated the null hypothesis that, 'The mean score of students in the incoming Grade 11 students is 81'. What would be the alternative hypothesis for this?
A teacher formulated the null hypothesis that, 'The mean score of students in the incoming Grade 11 students is 81'. What would be the alternative hypothesis for this?
If Sofia wants to check if the average daily usage of social media of her friends is same as the global average usage, what should be the correct alternative hypothesis? Assume that the gloval average usage is 142 minutes per day:
If Sofia wants to check if the average daily usage of social media of her friends is same as the global average usage, what should be the correct alternative hypothesis? Assume that the gloval average usage is 142 minutes per day:
Flashcards
Hypothesis Testing
Hypothesis Testing
A statistical method used for making decisions based on experimental data.
A hypothesis
A hypothesis
A proposed explanation, assertion, or assumption about a population parameter.
Null Hypothesis
Null Hypothesis
States that there is no difference between a parameter and a specific value; contains an equals sign.
Alternative Hypothesis
Alternative Hypothesis
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Level of Significance
Level of Significance
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Two-Tailed Test
Two-Tailed Test
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One-Tailed Test
One-Tailed Test
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Rejection Region
Rejection Region
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Non-Rejection Region
Non-Rejection Region
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Critical Value
Critical Value
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Type I error
Type I error
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Type II error
Type II error
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Study Notes
Most Essential Learning Competencies
- Illustrates the null hypothesis
- Illustrates alternative hypothesis
- Illustrates the level of significance
- Illustrates the rejection region
- Illustrates the types of errors in hypothesis testing
Hypothesis Testing
- Weigh alternatives, collection of evidence, and the decision-making process are basic processes used in testing hypotheses in statistics.
Activity: Keep Me Connected
- Averages daily social media usage worldwide among global internet users is 142 minutes.
- Claim A: Average daily usage of social media is assumed to be the same.
- Claim B: Average daily usage of social media is assumed to be higher than the global average.
Definition of Terms
- Hypothesis testing is a statistical method for making decisions using experimental data, especially in testing assumptions about a population.
- A hypothesis is a proposed explanation, assertion, or assumption about a population parameter or the distribution of a random variable.
- Examples of questions that can be answered with a hypothesis test:
- Does the mean height of Grade 12 students differ from 66 inches?
- Do male and female Grade 7 and Grade 12 students differ in height on average?
- Is the proportion of senior male students' height significantly higher than that of senior female students?
The Null and Alternative Hypothesis
- Null Hypothesis: Denoted as "H sub o", states that there is no difference between a parameter and a specific value, always containing some form of equality.
- Alternative Hypothesis: Denoted as "H sub a," it is the opposite of the null hypothesis, containing symbols like ≠, <, or >.
- The null hypothesis is the current value of the population parameter, which you hope to disprove in favor of your alternative hypothesis.
Illustrative Example: School Record Claim
- A school record claims incoming Grade 11 students have a mean math score of 81.
- Option 1:
- The mean score of incoming Grade 11 students is 81 (= 81).
- The mean score of incoming Grade 11 students is not 81 (≠ 81).
- Option 2:
- The mean score of incoming Grade 11 students has no significant difference with the mean score of her students (= ).
- The mean score of incoming Grade 11 students has a significant difference with the mean score of her students ( ).
Activity: Now It's Your Turn
- To formulate two hypotheses about global vs average usage of her Friends and if it is the same as global average, global average = 142
- HA. Is not equal to 142.
Example 1
- Claim: Average monthly income of Filipino families in the low-income bracket is P 7,500.
- H₀: Average monthly income is P 7,500 (μ = 7,500).
- Hₐ: Average monthly income is not equal to P 7,500 (μ ≠ 7,500).
- The null hypothesis is expressed using the "equal" symbol, because the claim does not specify any direction.
Example 2
- Claim: The average number of hours that a person who develops a COVID-19 symptom to improve without treatment is more than 2 weeks.
- H₀: The average number of hours that a person who develops a COVID-19 symptom to improve without treatment is 2 weeks. (μ = 2)
- Hₐ: The average number of hours that a person who develops a COVID-19 symptom to improve without treatment is more than 2 weeks. (μ > 2)
- Alternative hypothesis is expressed with a ">" symbol, indicating "more than/greater than."
Example 3
- Claim: Average number of hours that side effects of COVID-19 vaccines last is less than 48 hours.
- H₀: Average number of hours that side effects of COVID-19 vaccines last is 48 hours. (μ = 48)
- Hₐ: Average number of hours that side effects of COVID-19 vaccines last is less than 48 hours. (μ < 48)
- Alternative is expressed with "<" due to "less than" symbol.
Example 4
- Claim: No more than 60% of the registered voters in Bataan voted in the local election.
- H₀: No more than 60% of voters voted (μ ≤ 60).
- Hₐ: More than 60% of voters voted (μ > 60).
- The alternative is expressed with ">" showing "less than or equal to”.
Level of Significance
- Denoted by alpha (α), the degree of significance at which the null hypothesis is rejected.
- 100% accuracy is impossible.
- Significance level represents the probability of making a wrong decision when the null hypothesis is true.
- Common values for α are 1% (0.01), 5% (0.05).
Illustrative Example: Maria's Study
- Maria uses a 5% level of significance in proving that there is negligble change in average enrollment in the 10 sections for the last two years.
- This means there is a 5% chance the null hypothesis would be rejected when it is true.
Activity: Now It's Your Turn
- If Sofia used a 0.10 level of significance, she would have a 10% chance of a wrong conclusion if the two values have no significant difference (null hypothesis).
Two-Tailed vs One-Tailed Test
- Two-Tailed Test:
- Alternative uses a not-equal sign, where there is no assertion made on the direction of the difference.
- The rejection region is split into two equal parts, one in each tail.
- One-Tailed Test:
- Alternative uses "<" or ">". The critical rejection region lies entirely in one tail of the sampling distribution.
- It may be a right or left-tailed test.
Illustrative Examples: Registrar Believes Enrollee Number is
- Not the same as the previous year: Use a two-tailed test.
- Less than the previous year: Use a left-tailed test.
- Greater than the previous year: Use a right-tailed test.
Activity: Now It's Your Turn
- In relation to the two claims of Sofia regarding her usage of social media, type of test:
- For Claim A: Average is the same use a Two-Tailed test.
- For Claim B: Average is higher use a Left-Tailed Test.
Illustration of the Rejection Region
- The rejection region is a set of all values of the test statistic that causes us to reject the null hypothesis.
- The non-rejection or acceptance region is the set of all values of the test statistic that causes failure to reject or accept the null hypothesis.
- The critical value is a boundary on the test distribution, used to determine if the null hypothesis should be rejected.
Illustration Example 1: Sofia's Claim
- Sofia's claim assumes the average online usage of her friends is the same globally.
- It was computed for the t-value using t-value formula
- Given: = 142, = 152
- = 19.855 = 10
- Critical T Value is 2.262
- The T value lies in the non rejection-region.
- As The computed t-value is at the non-rejection region, we fail to reject the null hypothesis:
- H₀: The average online usage of her Friends is the same as global usage.
- Hₐ: The average online usage of her Friends is not the same as global usage.
Illustration Example 2
- A medical trial is conducted to test whether or not a certain drug reduces cholesterol level, and the Z value is computed and lies in the rejection area.
- Results: As the computed z-value lies in the rejection region, we reject the null hypothesis.
- H₀: The certain drug is effective in reducing cholesterol levels by 60%.
- Hₐ: The certain drug is not effective in reducing cholesterol levels by 60%.
Illustrative Example 3
- Sketch the rejection region of the test hypothesis with critical values of ±1.753
- Determine if the computed t-value of -1.52 lies in that region.
- Locate the computed t-value; since it is not in the rejection region, we fail to reject the null hypothesis, H₀ .
Type I and Type II Errors
- Type I error is rejecting the null hypothesis when it is true.
- Type II error is accepting the null hypothesis when it is false.
Error Summary
- Null Hypothesis IS true:
- A correct decision is failing to reject the null hypothesis.
- A type 1 error, is incorrectly rejecting the null hypothesis.
- Null Hypothesis is NOT true:
- A type 2 error is incorrectly failing to reject the null hypothesis.
- A correct decision is rejecting the null hypotheis.
Illustrative Example: Bryan's Food Cart
- Bryan is starting a food cart business and tests at a 5% significance level whether the demand is high enough to support his business before he applies for permits, and states:
- H₀: The demand is high enough.
- What would be the consequence of a Type I error in this setting?
- Bryan doesn't choose a city where demand is actually high enough.
- This is because Bryan rejected the true null hypothesis.
- What would be the consequence of a Type II error in this setting?
- Bryan chooses a city where demand isn't actually high enough.
- This is because Bryan failed to reject the false null hypothesis.
Illustrative Example 2: Resort Owner's Water Test
- A resort owner tests the water in the swimming pool daily.
- The hypotheses for the test are:
- H₀: The water quality is acceptable.
- Ha: The water quality is not acceptable.
- The hypotheses for the test are:
- Type I Error Consquence:
- The owner closes the pool when it needs to be closed is Type 1 Error
- Type II Error in Setting
- The owner does not close, and chooses B is the type 2 error
Illustrative Example 2 - Safety
In terms of safety:
- A Type II error (not closing the pool when it needs to be) has more dangerous consequences.
Activity; Now It's Your Turn
If Sofia finds that her null hypothesis is:
- True, and fails to reject it, it is a Correct Decision.
- True, and rejects it, she commits a Type I Error.
- False, and fails to reject it, she commits a Type II Error.
- False, and rejects it, she commits a Correct Decision.
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