A random sample of 20 healthy adults eating a traditional American diet is selected. They agree to adopt a vegetarian diet for 1 month. Based on their 20 sample cholesterol change values, a 95% one-sample t confidence interval for the population mean change in blood cholesterol level after switching diet is reported as the interval -27.9 to -11.6 mg/dl. If we use a matched-pairs t confidence interval in some statistical software with the 20 sample cholesterol values at the beginning of the study and the 20 sample cholesterol values at the end of the study, the resulting 95% confidence interval;a) could be narrower or wider but we cannot tell until we get the software output.b) would be much narrower.c) would be slightly narrower.d) would be exactly the same.e) would be much wider.f) would be slightly wider.

a factor that influences the width of the confidence interval, which is not modified by the researcher, is the variance, the greater the variance, the greater the interval, as well as the sample size modifies, the larger the sample, the interval will be narrower, for which in the case we can say that the number of people treated does not change, so the sample is the same, but 2 variables increase that were not previously considered, before and after cholesterol levels, so the interval will be a little wider.