Term
| What are the key properties of the normal distribution? |
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Definition
- Completely described by its mean and variance
- Skewness = 0 (symmetric around its mean)
- Kurtosis = 3
- A linear combination of normally distributed random variables is also normally distributed
- The probability of outcomes further above and below the mean get smaller and smaller but do not go to zero
- Confidence intervals can be constructed assuming a certain number of standard deviations from the mean
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Term
| The 90% confidence interval for X is: |
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Definition
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Term
| The 95% confidence interval for X is: |
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Definition
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Term
| The 99% confidence interval for X is: |
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Definition
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Term
| What's a standard normal distribution and how do you calculate it? |
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Definition
it's a normal distribution that has been standardized so that it has a mean of zero and a standard deviation of 1.
To standardise, a z value needs to be calculated. This represents the number of standard deviations a given observation is from the population mean.
Calculated by:
z = (observation - population mean) / standard deviation |
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Term
| Whats the Central Limit Theorem: |
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Definition
| states that for simple random samples of size n from a population with a mean u and a finite variance, the sampling distribution of the sample mean approaches a normal probability distribution (with mean and std deviation equal to population mean and std deviations) as the sample size becomes large. |
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Term
| What's the standard error of the sample mean? how do you calculate it? |
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Definition
it's the standard deviation of the distribution of the sample means.
= (standard deviation of the population) / square root of n where n = size of the population |
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Term
| What are the properties of the student's t distribution? |
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Definition
- symmetrical
- defined by a single parameter, the degrees of freedeom where df = number of sample observations minus 1 (i.e. n-1)
- less peaked than a normal distribution with fatter tails
- as df gets larger, the shape of the t-distribution approaches a normal distribution |
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Term
| When should the t distribution be used? |
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Definition
| small sample size (< 30) from populations with an unknown variance and an approximately normal distribution |
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Term
What is the chi-square test used for?
what does it require?
What is the calculation for the chi-square test statistic? |
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Definition
hypothesis tests concerning the variance of a normally distributed population.
Requires the use of a chi-square distributed test statistic.
chi-square distribution is asymmetrical and approaches normal distribution as df increase.
Χ2n-1 = (n-1)s2 / σ20
where n = sample size
s2 = sample variance
σ20 = hypothesised value for the population variance |
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Term
| Tell me about the F distribution? |
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Definition
used to test hypotheses concerned with teh equality of the variances of two populations.
Hypothesis testing using this distribution is referred to as the F test. |
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Term
| What are the assumptions of using the F test? |
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Definition
- populations from which samples are drawn is normally distributed
- samples are independent |
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Term
| How do you calculate the F statistic? |
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Definition
F = s12 / s22
s12 = variance of sample of n1 observations drawn from population 1
s22 = variance of sample of n2 observations drawn from population 2 |
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Term
| Whats the shape of the F distribution |
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Definition
| right skewed and is truncated at zero on teh left hand side. |
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