As the sample size of a group in a repeated-measures design increases, the t-distribution... more closely approximates the z-distribution becomes more platykurtic becomes more skewed has fewer degrees of freedom
Question
As the sample size of a group in a repeated-measures design increases, the t-distribution... more closely approximates the z-distribution becomes more platykurtic becomes more skewed has fewer degrees of freedom
Solution
As the sample size of a group in a repeated-measures design increases, the t-distribution more closely approximates the z-distribution.
Here's why:
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The t-distribution is a type of probability distribution that is symmetric and bell-shaped, like the standard normal distribution (z-distribution), but has heavier tails, meaning it has more values at the extremes.
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The shape of the t-distribution depends on the degrees of freedom. The degrees of freedom for a t-distribution is related to the sample size of the data set, with the degrees of freedom being equal to the sample size minus one.
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As the sample size increases, the degrees of freedom also increase. As the degrees of freedom increase, the shape of the t-distribution becomes more like the shape of the standard normal distribution.
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Therefore, as the sample size of a group in a repeated-measures design increases, the t-distribution more closely approximates the z-distribution.
The t-distribution does not become more platykurtic (having thinner tails and a lower peak than the normal distribution), more skewed (not symmetric), or have fewer degrees of freedom as the sample size increases.
Similar Questions
With more degrees of freedom a t-distribution becomes:Question 6Answera.More flat, with thicker tailsb.More left skewed, with a longer left tailc.More right skewed, with a longer right taild.More pointy, with thinner tails
How is the t-distribution similar to the standard z-distribution?
By coincidence, two experiments with an experimental group and a control group come up with the same t value. But one is based on 100 people total, and the other is based on 10 people total. The one with only 10 people, compared to the larger experiment, will have:Question 2Answera.A larger degrees of freedomb.A smaller standard errorc.A larger p-valued.A larger average of means
The student t-distribution approaches the normal distribution as the:Group of answer choicesnumber of degrees of freedom increases.sample size decreases.number of degrees of freedom decreases.the significance level increases.
When is a t-test preferred over a z-test in statistical analysis?*1 pointWhen the sample size is smallWhen dealing with categorical dataWhen comparing three or more groupsWhen the population standard deviation is known
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