1 Everyone believes that average height of people in your building is 67 inches. You want to check this, so you survey 100 people. You read in a science magazine that the variance for human height is 4 inches (and, of course, a 2 inch standard deviation). When you take your survey, you observe a mean of 68. Is this a statistically significant difference? What's the pvalue? 2 Everyone believes that average height of people in your building is 67 inches. You want to check this, so you survey 100 people. You don't know the population variance and need to infer it from the data. When you take your survey, you observe a mean of 68. You observe a sample variance of 4. Is this a statistically significant difference? What's the pvalue? 3 Everyone believes that average height of people in your building is the same as the average height of people in another building. You want to check this, so you survey 100 people in each building. (Note that you could sample different amounts of people in different buildings). You don't know the population variance for either building and need to infer it from the data. When you take your survey, you observe a mean of 68 for your building and a mean of 70 for the other building. You observe a sample variance of 4 in your building and 5 in the other building. Is this a statistically significant difference? What's the pvalue? 4 Everyone believes that average height of people in your building is the same as the average height of people in another building. You want to check this, so you survey 100 people in each building. (Note that you could sample different amounts of people in different buildings). You don't know the population variance for either building and need to infer it from the data. When you take your survey, you observe a mean of 68 and sample standard deviation of 3 for your building; and a mean of 70 and sample standard deviation of 5 for the other building. When you pool the variances, you need to determine if the two populations have the same variance. To do that you check if the ratio of the two sample variances behaves the way that ratio usually behaves. Are these two sample statistically different? What's the pvalue