Elementary statistics homework
Table 5—t-Distribution c-confidence interval Left-tailed test Right-tailed test Two-tailed test Level of confidence, c 0.80 0.90 0.95 0.98 0.99 One tail,α 0.10 0.05 0.025 0.01 0.005 d.f. Two tails,α 0.20 0.10 0.05 0.02 0.01 1 3.078 6.314 12.706 31.821 63.657 2 1.886 2.920 4.303 6.965 9.925 3 1.638 2.353 3.182 4.541 5.841 4 1.533 2.132 2.776 3.747 4.604 5 1.476 2.015 2.571 3.365 4.032 6 1.440 1.943 2.447 3.143 3.707 7 1.415 1.895 2.365 2.998 3.499 8 1.397 1.860 2.306 2.896 3.355 9 1.383 1.833 2.262 2.821 3.250 10 1.372 1.812 2.228 2.764 3.169 11 1.363 1.796 2.201 2.718 3.106 12 1.356 1.782 2.179 2.681 3.055 13 1.350 1.771 2.160 2.650 3.012 14 1.345 1.761 2.145 2.624 2.977 15 1.341 1.753 2.131 2.602 2.947 16 1.337 1.746 2.120 2.583 2.921 17 1.333 1.740 2.110 2.567 2.898 18 1.330 1.734 2.101 2.552 2.878 19 1.328 1.729 2.093 2.539 2.861 20 1.325 1.725 2.086 2.528 2.845 21 1.323 1.721 2.080 2.518 2.831 22 1.321 1.717 2.074 2.508 2.819 23 1.319 1.714 2.069 2.500 2.807 24 1.318 1.711 2.064 2.492 2.797 25 1.316 1.708 2.060 2.485 2.787 26 1.315 1.706 2.056 2.479 2.779 27 1.314 1.703 2.052 2.473 2.771 28 1.313 1.701 2.048 2.467 2.763 29 1.311 1.699 2.045 2.462 2.756 30 1.310 1.697 2.042 2.457 2.750 31 1.309 1.696 2.040 2.453 2.744 32 1.309 1.694 2.037 2.449 2.738 33 1.308 1.692 2.035 2.445 2.733 34 1.307 1.691 2.032 2.441 2.728 35 1.306 1.690 2.030 2.438 2.724 36 1.306 1.688 2.028 2.434 2.719 37 1.305 1.687 2.026 2.431 2.715 38 1.304 1.686 2.024 2.429 2.712 39 1.304 1.685 2.023 2.426 2.708 40 1.303 1.684 2.021 2.423 2.704 45 1.301 1.679 2.014 2.412 2.690 50 1.299 1.676 2.009 2.403 2.678 60 1.296 1.671 2.000 2.390 2.660 70 1.294 1.667 1.994 2.381 2.648 80 1.292 1.664 1.990 2.374 2.639 90 1.291 1.662 1.987 2.368 2.632 100 1.290 1.660 1.984 2.364 2.626 500 1.283 1.648 1.965 2.334 2.586 1000 1.282 1.646 1.962 2.330 2.581 ∞ 1.282 1.645 1.960 2.326 2.576 The critical values in Table 5 were generated using Excel. Unit VII Assignment: Hypothesis Testing for College Tuition Cost In this assignment, you will be using inferential statistics to determine if a claim about college tuition cost is accurate. According to the College Board’s website, the average tuition cost per year for a public four-year college (in-state cost) is $10,230. A) Assume that you disagree with the claim. Do you think the average tuition cost is higher? Or lower? The cost is higher. B) Using your answer in part A, write a set of hypotheses (null hypothesis and alternative hypothesis) to represent that claim and its complement. Replace the ?s below with the appropriate inequality signs (). Highlight the hypothesis that represents your claim. C) Gather data for tuition cost of 20 different universities. Assume the data you gather is normally distributed.How to Create your data set: Follow the directions to fill in the table below with 20 college’s tuition costs. · Navigate to https://www.collegetuitioncompare.com/compare/tables/ · In the drop down menus, ONLY select School Type as “Public School” and School Level as “4 year or higher.” Leave the rest of the drop down menus as is. Then select “update.” · Scroll down to the bottom of the list and for “Number of schools to show,” select “All.” · The list given will be in alphabetical order. You will be selecting 20 college tuition costs from this list. Do NOT just use the first 20 entries or even 20 consecutive entries. You will need to randomly select 20 entries from the entire list. Try to make sure you have a good range of tuition costs as well. · Write the tuition cost from the first column, “Tuition & Fees / In-State” for that college in the table below. 3565 3950 7410 4029 3505 11796 2830 7439 12620 11149 3957 4900 4740 11814 8400 9536 3683 10440 12330 12445 D) Calculate the mean and standard deviation of your data set. You may use technology such as Google Sheets, Excel, or a TI-83/TI-84. Round to the nearest hundredth. Mean _______7526.9_____ Standard Deviation _____3680.5___________________ E) Using a significance level , find the critical value using the following steps. 1. What are the degrees of freedom? 2. Will this be a one-tailed or two tailed test? 3. Using table 5 from the back of your textbook (page A18 in Appendix B), what is the critical value? F) Add the critical values to the graph below and shade the rejection region. (Special Instruction: For this part, it is recommended that you do this by hand. You can print out this page and use the image below as a template to write on or you can create a handwritten normal curve. Take a photo of your graph and replace the image below with it. If you need any technical assistance with this process, please email Waldorf’s tech support.) G) Calculate the test statistic. Replace the ?s in the formula with the appropriate values. Round to the nearest hundredth. H) Add the test statistic to your graph from part F, and insert the image below. I) What is the P-value? View the video Hypothesis Testing for the Mean (Sigma Unknown) Part II to learn how to use Google Sheets to calculate the P-value of a t-test (transcript for Hypothesis Testing for the Mean (Sigma Unknown) Part II video). J) Make a decision to reject or fail to reject the null hypothesis using either the test statistic or the P-value. Note that the same conclusion will be reached using either method. K) Interpret the decision in the context of the original claim. L) If you lower the level of significance to , does your decision change? Explain your reasoning. M) Describe the type I and type II errors that could occur in our test by completing each of the following statements. · A ____________ (type I, type II) error will occur when the actual mean of college tuition cost is ______________ (at most, at least) $10,230 but you reject the null hypothesis, . · A ____________ (type I, type II) error will occur when the actual mean of college tuition cost is ______________ (less than, greater than) $10,230 but you fail to reject the null hypothesis, .