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    How To Find Percentiles For A T-Distribution: Statistics For Dummies, 2nd Edition

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    Nielyn WP
    1. The t-distribution is used to estimate population parameters when sample sizes are small and the normal distribution cannot be assumed. 2. It describes the distribution of t-scores, which are calculated using the sample mean, population mean, sample standard deviation, and sample size. 3. As sample size increases, the t-distribution approaches the normal distribution, with smaller variance and values concentrated around the mean.

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    How To Find Percentiles For A T-Distribution: Statistics For Dummies, 2nd Edition

    Uploaded by

    Nielyn WP
    46 views5 pages
    1. The t-distribution is used to estimate population parameters when sample sizes are small and the normal distribution cannot be assumed. 2. It describes the distribution of t-scores, which are calculated using the sample mean, population mean, sample standard deviation, and sample size. 3. As sample size increases, the t-distribution approaches the normal distribution, with smaller variance and values concentrated around the mean.

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    percentiles, study this!

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    Percentiles

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    1. The t-distribution is used to estimate population parameters when sample sizes are small and the normal distribution cannot be assumed. 2. It describes the distribution of t-scores, which are calculated using the sample mean, population mean, sample standard deviation, and sample size. 3. As sample size increases, the t-distribution approaches the normal distribution, with smaller variance and values concentrated around the mean.

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    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    46 views5 pages

    How To Find Percentiles For A T-Distribution: Statistics For Dummies, 2nd Edition

    Uploaded by

    Nielyn WP
    1. The t-distribution is used to estimate population parameters when sample sizes are small and the normal distribution cannot be assumed. 2. It describes the distribution of t-scores, which are calculated using the sample mean, population mean, sample standard deviation, and sample size. 3. As sample size increases, the t-distribution approaches the normal distribution, with smaller variance and values concentrated around the mean.

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    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    of 5

    HOW TO FIND PERCENTILES FOR A T-

    DISTRIBUTION

    RELATED BOOK

    Statistics For Dummies, 2nd Edition

    When you want to find percentiles for a t-distribution, you can use the t-table. A percentile is a number on a statistical
    distribution whose less-than probability is the given percentage; for example, the 95th percentile of the t-distribution
    with n– 1 degrees of freedom is that value of

    whose left-tail (less-than) probability is 0.95 (and whose right-tail probability is 0.05).

    The t-table shows right-tail probabilities for selected t-distributions. You can use it to solve the following problems.

    Suppose you have a sample of size 10 and you want to find the 95th percentile of its corresponding t-distribution. You

    have n – 1= 9 degrees of freedom, so, using the t-table, you look at the row for df = 9. The 95th percentile is the

    number where 95% of the values lie below it and 5% lie above it, so you want the right-tail area to be 0.05. Move

    across the row, find the column for 0.05, and you get

    This is the 95th percentile of the t-distribution with 9 degrees of freedom.

    Now, if you increase the sample size to n = 20, the value of the 95th percentile decreases; look at the row for 20 – 1 =

    19 degrees of freedom, and in the column for 0.05 (a right-tail probability of 0.05) you find

    degrees of freedom indicate a smaller standard deviation and thus, the t-values are more concentrated about the

    mean, so you reach the 95th percentile with a value of t closer to 0.


    T-distribution is the most famous theoretical probability distribution in continuous family of
    distributions. T distribution is used in estimation where normal distribution cannot be used to
    estimate population parameters.

    1. 1. t distribution (Student’s t distribution)


    2. 2. In the previous discussions, it was shown that when the population is normally
    distributed, or when the sample size is large enough, the sampling distribution of
    the mean is normally distributed. And of course, the bell curve is very handy to
    use.
    3. 3. However, in many cases where we can only obtain small sizes, the normal
    distribution does not hold true. Instead, we use the t distribution which is the
    distribution of t-scores.
    4. 4. t = t score x = sample mean 𝝁 = population mean 𝑺 = sample standard
    deviation 𝒏 = sample size
    5. 5. EXAMPLE 1 Find the t-score for a sample size of 16 taken from a population
    with mean 10 when the sample mean is 12 and the sample standard deviation is
    1.5.
    6. 6. Degrees of freedom - the number of observations in a data set that are free to
    change without changing the mean. For a single group test 𝑑𝑓 = 𝑁 − 1 For 2-
    group tests 𝑑𝑓 = 𝑁1 + 𝑁2 − 2
    7. 7. PROPERTIES of a t distribution 1. The distribution has mean 0. 2. The
    distribution is symmetric about the mean. 3. The variance is equal to 𝑑𝑓 𝑑𝑓−2 . 4.
    The variance is always greater than 1, but approaches 1 when df gets bigger.
    8. 8. What if n approaches infinity? The t distribution also approaches the standard
    normal distribution.
    9. 9. Increasing the sample size will….
    10. 10. Increasing the degrees of freedom will…
    11. 11. Increasing the degrees of freedom and sample size will make the t
    distribution approach a normal distribution.
    12. 12. The critical value is the thin line between rejection and acceptance.
    13. 13. The confidence interval is actually the acceptance region.
    14. 14. The t TABLE 1. The critical region appears at the top. 2. The degrees of
    freedom are on the leftmost section. 3. Confidence interval are at the bottom.
    15. 15. EXAMPLE 2 Find the t-score below which we can expect 99% of sample
    means will fall if samples of size 16 are taken from a normally distributed
    population.
    16. 16. EXAMPLE 2 SOLUTION 1 − 𝛼 = 0.99 𝛼 = 0.01 𝑑𝑓 = 𝑛 − 1 𝑡0.99 = −𝑡0.01 𝑑𝑓
    = 15 𝑡0.99 = −𝑡0.01 = −2.602
    17. 17. EXAMPLE 3 If a random sample of size 25 drawn from a normal population
    gives a mean of 60 and a standard deviation of 4, find the range of t- scores
    where we can expect to find the middle 95% of all sample means.
    18. 18. EXAMPLE 4 Compute the probability that 𝑃 (−𝑡0.05 < 𝑡 < 𝑡0.10).

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