# Experiment Design & Analysis _SOLUTION

Option A: Assume that the one-way commute time of an U student from his or her home to their class at the U is a normally distributed random variable which we will call X. Furthermore, assume that the population standard deviation of X is σ0 = 10 minutes. Let µ be the unknown population mean for X. In part (g), you will use µ0 = 20 minutes. Option B: Come up with your own random variable X. For example, it could be the resistance of a resistor, or the run time of a particular executable. State an initial assumption for the population standard deviation of X, which you will call σ0. State an initial hypothesis for the mean of X, calling it µ0. Note that your assumed values may or may not be correct – they are a good guess and a starting point for this assignment. These values σ0 and µ0 could be a from a data sheet, or from an expert’s opinion (it may be that you are the expert). Note: If your random variable is anything asked of a person, please do not ask any private or sensitive information, and ask your instructor if there is any possibility for concern.l1. State which option you are doing (A or B, not both). If B, state what your random variable X is, and state your assumptions for the population standard deviation and population mean, σ0 and µ0. 2. Experimental design: Determine a minimum sample size such that we will be 95% conﬁdent that the error will not exceed σ0/2 when the sample average ¯ X is used to estimate the population mean µ. Let n denote this sample size. 3. Population: From what population are you sampling? For Option A the population might be: UofU students in the class, or your UofU student friends on facebook, for example. Describe how you collect the data – make sure this samples from your chosen population. 4. Data Collection: Collect a sample of n from among your chosen population, and record their answers. 5. Mean Estimation I: Based on your sample, and your assumed known standard deviation σ0, ﬁnd a 95% conﬁdence interval for µ. (Assume the central limit theorem applies.) 6. Mean Estimation II: Now assume that you don’t know the population standard deviation, and use the t-distribution and the sample standard deviation S to ﬁnd a 95% conﬁdence interval for µ. 7. Test Hypothesis: Test the null hypothesis that the mean of X is µ0 at the signiﬁcance level α = 0.01. The alternate hypothesis is that the mean commute time is not µ0. You may assume that the standard deviation of X is known to be σ0.

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