Exam 11: Confidence Intervals and Hypothesis Tests Based on Two Samples or Treatments

If the underlying populations are normally distributed and both population variances are equal, the test statistic ​ ​ Follows a:

Suppose two samples of sizes 25 and 35, respectively, are independently drawn from two populations that are both normally distributed.Also assume the population variances are unknown but equal.What is the number of degrees of freedom that the t test statistic would have?

Concerning inference on two population proportions, it is appropriate to use the pooled or combined estimate of the common population proportion when:

A small town claims that it needs rezoning to accommodate its current growth.The town wants to re-designate a current residential area as commercial.To gain approval from the zoning commission, it must show that the commercial taxes paid in this area are significantly higher, on average, than those paid in other residentially zoned areas.A random sample of 16 dwellings in standard residential areas (sample 1) yields an average commercial tax of $25,000 with a standard deviation of $11,000.A sample of 15 dwellings in the "rezoned" area (sample 2) has an average commercial tax of $55,800 with a standard deviation of $2500.Assume that the populations in question are both normal and have unequal variance.Construct a 90% confidence interval on the population mean difference in commercial taxes between the two areas.

If two samples are combined by matching each individual or object in sample 1 with a similar object/individual in sample 2, the resulting single sample is: