PHC410 Biostatistics Probability Distributions
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Questions and Answers

What is the formula for mean in a probability distribution?

  • Mean, μ = n(1-p)
  • Mean, μ = np (correct)
  • Mean, μ = p/n
  • Mean, μ = np(1-p)

Which of the following represents the variance in a probability distribution?

  • Variance, σ² = np(1-p) (correct)
  • Variance, σ² = p(1-n)
  • Variance, σ² = np²
  • Variance, σ² = np

If p = 0.2 and n = 4, what is the probability of getting exactly 3 successes?

  • 0.4096
  • 0.2048 (correct)
  • 0.1024
  • 0.5120

Which of the following components is NOT required to calculate the variance in a binomial distribution?

<p>Number of successes (x) (A)</p> Signup and view all the answers

In a binomial distribution, what does the symbol 'p' represent?

<p>The probability of success (C)</p> Signup and view all the answers

What decision is made when failing to reject a true null hypothesis?

<p>Correct decision (D)</p> Signup and view all the answers

Which type of statistical test is appropriate when you want to determine if a mean is significantly greater than a specified value?

<p>Right-tailed test (A)</p> Signup and view all the answers

What happens if you reject a true null hypothesis?

<p>Wrong decision (C)</p> Signup and view all the answers

In a left-tailed test, what symbol indicates the direction of the hypothesis statement?

<p>&lt; (B)</p> Signup and view all the answers

What is the probability of committing a Type II error (β) when failing to reject a false null hypothesis?

<p>β (A)</p> Signup and view all the answers

Which of the following correctly describes a two-tailed test?

<p>Tests for both increases and decreases (D)</p> Signup and view all the answers

Which of the following is a characteristic of a right-tailed test?

<p>It has a hypothesis that states a parameter is greater than a specified value. (A)</p> Signup and view all the answers

What denotes a correct decision when rejecting a false null hypothesis?

<p>Correct decision (D)</p> Signup and view all the answers

What is a key disadvantage of the sampling procedure that relies on initial respondents providing information about additional respondents?

<p>It introduces bias due to the lack of independence among sampling units. (B)</p> Signup and view all the answers

What is defined as a null hypothesis?

<p>A general statement asserting that there is no relationship between two variables. (B)</p> Signup and view all the answers

Why is it typically easier to disprove the null hypothesis than to prove it true?

<p>Disproving the null requires only one counterexample. (A)</p> Signup and view all the answers

Which of the following best represents an alternative hypothesis?

<p>Higher educational attainment leads to increased income. (C)</p> Signup and view all the answers

In a non-probability sampling method, what is a primary concern regarding sample representation?

<p>It may not accurately represent the larger population. (B)</p> Signup and view all the answers

What is the purpose of using tests for statistical significance in research?

<p>To evaluate whether the results are due to chance or a true relationship (C)</p> Signup and view all the answers

When we say a result is statistically significant, what does it imply?

<p>The probability of the result occurring by chance is low (C)</p> Signup and view all the answers

What does rejecting the null hypothesis imply in hypothesis testing?

<p>There is an observed relationship between the variables studied (D)</p> Signup and view all the answers

What is indicated by a significance level of 0.05 in hypothesis testing?

<p>There is a 5% chance of making a Type I error (B)</p> Signup and view all the answers

Which of the following statements about null and alternative hypotheses is true?

<p>The null hypothesis represents the expected outcome in research (C)</p> Signup and view all the answers

Which of the following is a common source of error that can affect the validity of research findings?

<p>Researcher bias during data interpretation (A)</p> Signup and view all the answers

What is meant by the term 'confidence level' in hypothesis testing?

<p>The probability of correctly rejecting the null hypothesis when it is false (C)</p> Signup and view all the answers

What does it mean when a researcher states they do not reject the null hypothesis?

<p>There is a lack of evidence to support the alternative hypothesis (A)</p> Signup and view all the answers

Flashcards

Probability Distribution

A statistical function that describes all the possible outcomes of a given random variable and their probabilities.

Binomial Distribution

A probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials.

Mean (μ)

The expected value of a binomial distribution, calculated as μ = np where n is the number of trials and p is the probability of success.

Variance (σ²)

The average squared difference from the mean, calculated in a binomial distribution as σ² = np(1-p).

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Bernoulli Trials

A series of independent experiments or events with only two possible outcomes (success or failure).

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Null Hypothesis (H0)

A statement of no effect or no relationship between variables in a research study.

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Alternative Hypothesis (HA)

A statement that there is an effect or relationship between variables in a research study.

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Statistical Significance

A measure of how likely a result is due to chance, not a true effect.

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Probability of being wrong

The likelihood that a researched relationship is due to random chance, and not a real effect.

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Test of Significance

Statistical tools used to determine if a relationship between variables is likely due to a true effect, or if it occurred by chance.

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5% or 0.05 Significance Level

Indicates a 95% confidence level that a relationship is real, not due to chance.

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Reject the Null Hypothesis

Conclusion drawn when the probability of a relationship arising by chance is low enough (e.g., 5% or below).

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Confidence Level

The percentage of times a test will give the correct result if repeated many times under similar conditions.

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Null Hypothesis (H0)

A statement that there's no relationship or effect between variables being studied.

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Alternative Hypothesis (HA)

A statement that there is a relationship or effect in the research.

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Sampling Procedure

Methods used to select a representative group from a larger population for study.

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Sampling bias

Error in sampling that occurs when the sample is not truly representative of the overall population, often due to methods used.

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Projecting data beyond sample

Making predictions about a population based on a limited sample is unfounded.

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Null Hypothesis Rejection

Rejecting a null hypothesis when it's actually true. This is a Type I error.

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Type II error

Failing to reject a false null hypothesis.

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One-tailed test

A statistical test where the critical region is on one side of the distribution (either greater than or less than a certain value).

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Right-tailed test

A one-tailed test where the critical region is on the right side of the distribution.

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Left-tailed test

A one-tailed test where the critical region is on the left side of the distribution.

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Two-tailed test

A statistical test with critical regions on both sides of the distribution, testing for difference in either direction.

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Correct Decision (Null Hypothesis)

Failing to reject a true null hypothesis.

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Decision rule (right-tailed)

Reject the null hypothesis if the test statistic is greater than the critical value.

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Study Notes

Course Title

  • PHC410 Pharmaceutical Biostatistics

Probability Distributions

  • A function that describes likelihood of possible values a random variable can take
  • Expressed in a graph, table or formula
  • Discrete distributions: Binomial, Poisson
  • Continuous distributions: Normal

Random Variables

  • Represented by X
  • Variables with numerical outcomes of a random phenomenon
  • Example: Probability when rolling a die = 1/6

Types of Random Variables

  • Discrete Variables:
    • Countable numbers (integers)
    • Examples: dead/live, treatment/placebo, dice counts, marital status
  • Continuous Variables:
    • Infinite values (continuous scale)
    • Examples: blood pressure, weight, speed of a car, drug concentration

Probability Distribution Function (PDF)

  • Maps possible values of X against their probabilities of occurrence (P(x))
  • P(x) is a number between 0 and 1.0
  • Total area under a probability function is always 1

Discrete Distribution Functions

  • p(x) represents probability of a random variable having specific value x
  • Examples: rolling a six-sided die, showing outcomes 1 to 6 with probability 1/6
  • ΣP(x) = 1 for all x

Cumulative Distribution Function (CDF)

  • Represents the cumulative probabilities up to a given value
  • Example, probability of rolling 3 or less
  • P(X ≤3) = 1/2

Examples for Cumulative P(X)

  • What's the probability of rolling a 3 or less? P(x≤3)=1/2).
  • What's the probability of rolling a 5 or higher? P(x≥5) = 1 - P(x≤4) = 1-2/3=1/3
  • Specific problems like A) exactly 14 ships arrive, B) at least 12 ships arrive, and C) at most 11 ships arrive.

Binomial Distributions

  • Deal with dichotomous outcomes (success/failure)
  • Fixed number of trials, same probability of success for each trial, trials independent.
  • Formula : P(x) = n! / ((n-x)! x!) * p^x * q^(n-x)
  • Key elements:
    • n = number of trials
    • x= number of successes in n trials
    • p= probability of success in one trial
    • q= probability of failure in one trial (q = 1-p)
  • Mean = np, Variance = np(1-p)
  • Can be obtained by specific formulas, computer software, binomial tables or online calculators

Poisson Distributions

  • Describes rare events over a specific interval (e.g., time, distance, area, volume).
  • Occurrences random, independent, and uniformly distributed
  • Formula : P(X) = (e^-λ) * (λ^x) / x!
  • λ= average number of successes in an interval
  • Examples include radioactive decay, arrivals of people in a line.
  • Can be calculated using specific formulas, computer software, Poisson tables or online calculators

Normal Distributions

  • Bell curve shape, symmetric, fits phenomena like human height and IQ scores
  • Defined by mean (μ) and standard deviation (σ)
  • Standard normal distribution (Z): Mean = 0, Standard deviation = 1.

Z-tables

  • Used to find probabilities for standard normal distributions
  • Useful to calculate probabilities when working with normal distributions of different means or standard deviations.
  • Provides Cumulative Area from the Left and Z-Score

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Related Documents

PHC410 Pharmaceutical Biostatistics PDF
Sampling Distribution & Hypothesis Testing Lecture Notes PDF

Description

This quiz covers the essentials of probability distributions in pharmaceutical biostatistics. It includes concepts related to discrete and continuous random variables, the probability distribution function, and examples of various distributions. Test your understanding of how these principles apply in a pharmaceutical context.

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