[MUSIC] The General Social Survey asks," for how many days during the past 30 days was your mental health, which includes stress, depression, and problems with emotions not good?" Based on responses from 1,151 US residents, the survey reported a 95% confidence interval of 3.40 to 4.24 days in 2010. Interpret this interval in context of the data. Remember, the confidence interval, is always about the unknown population mean, and the confidence level, tells us how confident we are, that this particular interval captures that mean. Then, we are 95% confident, that Americans on average, have 3.40 to 4.24 bad mental health days. Per months. Here we have another question based on the same data set. We are asked, in this context, what does a 95% confidence level mean? It is always very important to try to put all of the concepts and terminology you learn in context of the data that you're working with. And if you're able to do so, that means that you really fully comprehend the material. Remember that generically a 95% confidence level means. That 95% of confidence intervals, created based on random samples of the same size from the same population will contain the true population parameter. So in this context, what that means is that, 95% of random samples of 1151 Americans will yield confidence intervals that capture the true population mean of number of bad mental health days per month. Suppose the researchers think a 99% confidence level would be more appropriate for this interval. Will this new interval be narrower or wider than the 95% confidence interval? Remember, that as the confidence level increases, so does the width of the confidence interval. So, we're actually going to end up with a wider confidence interval if we use a 99% confidence level. Instead of a 95%. Next we have a different question based on a different set of real data. A sample of 50 college students were asked, how many exclusive relationships they've been in so far? The students in the sample had an average of 3.2 exclusive relationships, with a standard deviation of 1.74. In addition, the same distribution was only slightly skewed to the right. Estimate the true number of exclusive relationships based on this sample using a 95% confidence interval. So we're given that 50 college students are in the sample, so N is equal to 50. They had an average of 3.2 exclusive relationships. So the sample mean is 3.2, with a standard deviation of 1.74, so the sample standard deviation is 1.74. We have all of our building blocks to calculate the confidence interval now. However we must first check to make sure that the conditions required to use the confidence interval technique we just learned are actually met. First, we have a random sample and 50 is certainly less than 10% of all college students. Therefore, we can assume that the number of exclusive relationships one student in the sample has been in, is independent of another. So we have independent observations with respect to the variable that we're interested in. Second, the sample size is greater than 30, and the distribution of the sample is not so skewed. Indicating that the population distribution of number of exclusive relationships of all college students is likely not so skewed either. Then we can assume, that the sampling distribution of average number of exclusive relationships. From samples of size 50 will be nearly normal. So the required conditions are met and we can move on to the calculations. [BLANK_AUDIO] We first need to calculate the standard error since we will need this value to calculate then the margin of error. We know that the standard error is s over square root of n which in this case is going to be 1.74 divided by square root of 50 which comes out to be approximately .246. Then the 95% confidence interval can be calculated as. The sample mean of 3.2 plus or minus 1.96, the critical value, times 0.246, the standard error. That makes 3.2 plus or minus our margin of error of 0.48. And the bounds of the confidence interval are then going to be 2.72 to 3.68. Meaning that we are 95% confident. That college students on average have been in 2.72 to 3.68 exclusive relationships.