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STATS quiz 3
| Question | Answer |
|---|---|
| What is a t score? | A t-score is a standardized value that tells us how far our sample mean is from the hypothesized population mean in terms of standard errors |
| What is the purpose of a t score/when is it used? | 1. When the population standard deviation is unknown 2. The sample size n is small (typically n<30) |
| Degrees of Freedom | every t-distribution has a df. It represents how much independent information is available in your data to estimate variability |
| What is the degrees of freedom for a single sample mean | df=n-1 where n is the sample size |
| The t distribution accounts for | extra uncertainty when we estimate standard deviation using the sample standard deviations |
| The shape of the t distribution depends on | the degrees of freedom |
| Smaller df (sample size) the curve is | wider and flatter |
| Larger df (large sample size) the curve becomes | narrower and more like the standard normal (z) curve |
| A t-score is | Just like a z-score, a t-score tells us how "extreme" our sample mean is but it uses s (sample standard deviation) instead of sigma (population standard deviation |
| z-distribution used when | population standard deviation is known |
| shape of z-distribution | bell shaped, symmetric |
| spread of z-distribution | constant |
| spread of t-distribution | depends on sample size (n) through degrees of freedom (df=n-1) |
| As n increases the z-distribution | stays the same |
| As n increases the t-distribution | becomes more like the z-distribution |
| The t table handout reads differently than the z table | It only can give t-values for certain areas to the RIGHT and the t-value is found by looking inside the table. Since the table is symmetrical, if its an area to the left that we are looking for, we would look this area up to the right and make it negative |
| Statistical Inference is the process of | 1. Taking a sample from a larger population 2. Analyzing that sample 3. Using the results to make claims about the population from which the sample mean was drawn |
| Population Parameter | examines how a population mean relates to a specific value |
| Hypothesis testing | is one of the most important tools in statistical inference. It allows us to use sample data to test claims or ideas about population parameters |
| Hypothesis testing can be applied to many types of parameters: | Population mean, population proportion, median, difference between means, regression coefficients |
| Level of significance | The probability of rejecting the null hypothesis when it is actually true (Type 1 error) |
| Null hypothesis | represents no effect or no difference. =, less than or equal to, greater than or equal to |
| Alternative hypothesis | represents what you want to test or find evidence for. does not equal, less than, greater than |
| Sampling distribution | is the distribution of all possible sample means that we could get if we repeatedly took samples of the same size (n) from the population. |
| sampling distribution acts as | a bridge between what we observe in our sample (sample mean) and what is true in the entire population (the population mean) |
| small p value | evidence against null hypothesis-reject null |
| large p value | insufficient evidence-fail to reject null |
| two-tailed test | we are testing whether the sample mean is significantly different from the hypothesized mean- IN EITHER DIRECTION |
| p-value | the p values represents the probability of obtaining a sample statistic as extreme or more extreme than the one observed, assuming the null is true |
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user-1996284