1. A local tax assessor wants to determine if the housing values are different in two separate neighborhoods. The assessor was provided with the summary statistics for each neighborhood. In neighborhood 1, a sample of 32 homes has a mean selling price of $152,000. Oh the other side of town, a sample of 35 homes, in neighborhood 2, had a mean selling price of $154,000. From a prior study, neighborhood 1 had a standard deviation of $5,000 and neighborhood 2 had a standard deviation of $6,500. Using a 5 percent level of significance, can we conclude that the housing values in these two neighborhoods are statistically different?
2. Suppose the tax assessor picks neighborhood 3 and wants to see if its housing values are higher than that found in neighborhood 1. In neighborhood 3, the sample of 31 homes showing a mean selling price of $155,000, with a standard deviation of $6,000. At the 5 percent level of significance, can we conclude that the selling prices in neighborhood 3 are greater than that in neighborhood 1?
3. Assume that our tax assessor does not have the population standard deviations. Assume the assessor has a sample of data for 25 homes from neighborhood 1 and 25 homes from neighborhood 2. Sample standard deviation for neighborhood 1 is 4,576 and sample standard deviation for neighborhood 2 is 6,059. Using a 5 percent level of significance, can we conclude that the housing values in these two neighborhoods are statistically different?
4. Assume that our tax assessor has 25 observations from neighborhood 1 and 20 observation from neighborhood 3. The mean price in neighborhood 3 is $155,670 with a standard deviation of $5,968. Assume that the population variances are equal. Using a 5 percent level of significance, can we conclude that the housing values in these two neighborhoods are statistically different?
5. Assume that with have 25 observations from neighborhood 1 and we want to compare it to a sample of 30 observations from neighborhood 4. The sample of 25 for the neighborhood 1 has a mean of $152,444, with a standard deviation of $4,576. The sample of 30 homes in neighborhood 4 has a mean of $155,040, with a standard deviation of $6,750. We want to test the hypothesis that the values in neighborhood 1 are less than those in neighborhood 4 at the 5 percent level of significance.