Of the following, which shows how the general t statistic can be written?Question 1Answera.b.t = (estimate– hypothesisedvalue)c.d.
Question
Of the following, which shows how the general t statistic can be written?Question 1Answera.b.t = (estimate– hypothesisedvalue)c.d.
Solution
The general t statistic can be written as:
t = (estimate - hypothesised value) / standard error
Here's the step by step breakdown:
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Estimate: This is the point estimate of the population parameter you're interested in. For example, if you're trying to estimate the mean weight of all apples in a certain orchard, your estimate might be the mean weight of a sample of apples you took from that orchard.
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Hypothesised value: This is the value of the population parameter under the null hypothesis. For example, if your null hypothesis is that the mean weight of all apples in the orchard is 150 grams, then 150 grams is your hypothesised value.
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Standard error: This is a measure of the variability of your estimate. It's calculated differently depending on what kind of estimate you're dealing with. For a mean, for example, the standard error would be the standard deviation of your sample divided by the square root of the sample size.
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The difference between the estimate and the hypothesised value is calculated. This is the numerator of the t statistic.
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The standard error is calculated. This is the denominator of the t statistic.
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The t statistic is then calculated by dividing the difference from step 4 by the standard error from step 5. This gives you a measure of how many standard errors away from the hypothesised value your estimate is.
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