We will create an answer Excel spreadsheet to write the solution to our problems. After writing your name and Module 5 in the first two rows of the left-hand column and then skipping a row, label cell a4 as “Problem 1” and do likewise after we solve each one. Always start a hypothesis problem with stating the null and alternative hypothesis, in this case: Ho: μp = μnp ; Ha: μp > μnp and α = .05 . Find the c.v., which is a t-value with 99 degrees of freedom, 1.66. You need to find the sample mean and sample standard deviation of home with pools, those without pools and write these on you answer spreadsheet. Sorting column E will provide you with the raw information you need. We not know the population standard deviation, so, we must use a t-distribution to find the S.T.S. The standardized test statistic is t = { (ā1 – ā2) – (μ1 - μ2) } / √ (s12 /n1 + s22 /n2 ) = Observed difference – Hypothesized difference Standard error This formula assumes the variances are not equal, just like when we use a normal dist. Compare this to the c.v. or calculate the p-value. State your conclusion. For Problem 2, we need to create a new column, which will be the difference between column J from K, or vice-versa. Find the mean and standard deviation of the difference column and write these on your answer spreadsheet right after stating the null and alternative hypothesis. We have only sample data therefore, we must use a t-distribution. Find the c.v. on this two-tail test, which I come up with as ± 1.984. Determine the standardized test statistic, t = (ā - μā ) / (s /√n) , compare them, reject or fail-to-reject the null hypothesis and then state your conclusion. In Problem 3, after stating the null and alternative hypothesis, Ho: pb = po , Ha: pb > po , α = .05 , you may first sort column E and then sort column F. Calculate p-hat for both the proportion of brick homes with pools and the proportion of (other + frame) homes with pools. Find the c.v. for a z-distribution; i.e., z = 1.645. Test statistic is ̂p1 - ̂p2, the Standardized Test Statistics is z = {(̂p1 - ̂p2) – (p1 - p2)} / √ (p¯• q¯ (1/n1 + 1/n2)) p¯ = (x1 + x2) / (n1 + n2) = (n1̂̂p1 + n2 ̂p2) / (n1 + n2) = the weighted estimate Reject or fail-to-reject the null hypothesis and state your conclusion. In Problem 4, we need to add the Data Analysis tool to our display. We are going to set up the Data Analysis tool under the “Data” tab. Start by going to “File”, then all the way at the bottom, “Options”, then on the left highlight “Add-ins” and hit “Go” not enter, highlight Analysis Data Pak and hit Go, when the pop-up window appears check Analysis Data Pak and hit OK. This will now show up under the “Data” tab and be the right most entry. For Apple computers, start by going to “Tools” and then “add-ins”. On your answer spreadsheet, label four columns, two-bedroom, three-bedroom, etc. Sort column B on the data sheet. Using the ctrl c capability of your computer, copy column I for all the two-bedroom homes onto your answer spreadsheet. Do likewise for three, four and five-bedroom homes. Arrange each of these columns in ascending order; i.e., the smallest column to the largest. State your null hypothesis and alternative; i.e., Ho: All the means are the same; Ha: At least one mean is different. α = .05. With Data Analysis installed, go to “ANOVA Single Factor” and fill in the Input Range. Put in the first entry on your spreadsheet : the last entry; i.e., you are sweeping your ordered array. The Output Range is where on the page you want all the information that Excel will provide. When initiated, the Between Groups shows the degrees of freedom—the number of variables minus one, the F standardized test statistic, the F critical value and the p-value. State your conclusion comparing the p-value and α.