Construct a confidence interval to estimate a population mean when conditions are met. Interpret the confidence interval in context.
The SAT is the most widely used college admission exam. (Most community colleges do not require students to take this exam.) The mean SAT math score varies by state and by year, so the value of µ depends on the state and the year.
Is smoking during pregnancy associated with premature births? To investigate this question, researchers selected a random sample of 114 pregnant women who were smokers. The average pregnancy length for this sample of smokers was 260 days. From a large body of research, it is known that length of human pregnancy has a standard deviation of 16 days.
The test statistic tells you how different two or more groups are from the overall population mean, or how different a linear slope is from the slope predicted by a null hypothesis. Different test statistics are used in different statistical tests.
Statistical significance is a term used by researchers to state that it is unlikely their observations could have occurred under the null hypothesis of a statistical test. Significance is usually denoted by a p -value, or probability value.
Non-parametric tests don’t make as many assumptions about the data , and are useful when one or more of the common statistical assumptions are violated. However, the inferences they make aren’t as strong as with parametric tests.
They can be used to: determine whether a predictor variable has a statistically significant relationship with an outcome variable. estimate the difference between two or more groups. Statistical tests assume a null hypothesis of no relationship or no difference between groups.
Parametric tests usually have stricter requirements than nonparametric tests, and are able to make stronger inferences from the data. They can only be conducted with data that adheres to the common assumptions of statistical tests.
T-tests are used when comparing the means of precisely two groups (e.g. the average heights of men and women).
Independence of observations (a.k.a. no autocorrelation): The observations/variables you include in your test are not related (for example, multiple measurements of a single test subject are not independent, while measurements of multiple different test subjects are independent).
Here, we assume that 's are observed values of a random variable . Therefore, we can summarize our model as where is a random variable independent of . First, we take expectation from both sides to obtain Thus, Next, we look at , Therefore, we obtain Now, we can find and if we know , , .
Let's look again at the above model for regression. We wrote where is a random variable independent of . Note that, here, is the only variable that we observe, so we estimate using . That is, we can write The error in our estimate is Note that the randomness in comes from two sources: and .
a. H 0: μ = 10#N#b. H a: μ ≠ 10#N#c. Consider, X ¯ be the random variable which represents "the mean number of sick days employees took for the past year".#N#d. Student's t-distribution#N#e. − 1.12#N#f. 0.3#N#g. see the sketch#N#h. 0.05#N#i. ( 4.94, 11.81)
Hello. Welcome to the video. And today we're talking about hypothesis tests at specifically how to know when we can or cannot sufficiently reject the null hypothesis.
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Has your PS career progressed as you hoped and how challenging was it to move forward?