Unit 4B Project(3)

Congrats on making it to the final project! I hope you have found this class interesting and valuable. Our last project is focused on the last 3 chapters of our textbook dealing mostly with testing hypotheses. We are very skilled now in estimating the population parameter for mean or proportion based on our sample data. Now we want to take it one step further and test our sample data against what we might expect to see. For instance, if the average course grade in MA215 is generally 85%, but changes were made to the class to improve that grade, we would collect a sample and compare it to the 85% that we expect to see. In your Hawkes coursework you will determine how best to do this. One thing to keep in mind throughout the project is that I want you to create confidence intervals that correspond to your hypothesis test. Many get confused when determining the correct level of confidence. Here is what you should keep in mind: If I perform a left-tailed test using an alpha level of 0.05, then to create a corresponding confidence interval to give us the values we might expect to see, we would need to think about putting the same area on the right of our model, as well. So instead of creating a 95% confidence interval (which is what we would normally do with an alpha level of 0.05), we would create a 90% interval, leaving 5% in each tail. However, if I performed a 2-tailed test (where the alternative hypothesis is "not equal to") with an alpha level of 0.05, then I would use a 95% interval to back up my results. Be qu We ev Fo div va Fo Fo Fo No pu Fo so Be ea Als

A Sample Proportion (p-hat) 0.364667747 Formula Expected Proportion (p) 0.32Data Entry 1 - p 0.68 Formula Sample Size (n) 1234Data Entry 1 pt Z-Score 3.363738171 Formula 1 pt Probability (right tailed) 0.000384472 Function Inputs 1 pt e sure you are paying attention to what is expected in each cell. For instance, lets say I wanted to answer the uestion: We expect 32% of plain M&M's to be brown. In a sample of 1234 M&M's, we found 450 to be brown. Is this vidence that the M&M factory produces more than 32% brown M&M's? or our sample proportion (formula), I would enter =450/1234. Notice that the cell contains the solution to tha vision problem, but if I click on it, I can see that I entered 450/1234. For a formula we will enter = and then so alue to be calculated. or expected proportion (data entry), I simply enter 0.32 from the question, as that is what we expect. or 1-p (formula), I use =1-Y3, which gives me 0.68 as a solution. or sample size (data entry) I enter 1234, which is the size of the sample. ow, for z-score I am going to use all of the inputs I just entered. So intead of typing them all in again, I will sim ut =(Y2-Y3)/SQRT(Y3*Y4/Y5) and let Excel calulate the z-score for me. or probability (right tailed), which is a function, I will enter 1-NORM.S.DIST(Y6,1). Remember a function uses omething like NORM.S.DIST or STANDARDIZE or some other Excel function. e sure you are utilizing the inputs, even if they aren't graded, and paying attention to what I will be looking for ach cell: formula, data entry or function. so, recall that non-graded cells are locked so that all items to be graded are contained within the cell itself

Name Drop (ft) Speed (mph) Millennium Force 300 93 Goliath 255 85 Titan 255 85 Phantom's Revenge 228 82 Xcelerator 130 82 Desperado 225 80 HyperSonic XLC 133 80 Nitro 215 80 Phantom's Revenge 225 80 Son Of Beast 214 78.4 Superman - Ride Of Steel 221 77 X 215 76 Mamba 205 75 Steel Force 205 75 Wild Thing 196 74 Apollo's Chariot 210 73 Raging Bull 208 73 Rattler 166.5 73 Superman - Ride Of Steel 205 73 Magnum XL-200 194.6 72 Viper 171 70 Volcano The Blast Coaster 80 70 Great American Scream Machine 155 68 Alpengeist 170 67 Incredible Hulk 105 67 Manhattan Express 144 67 Boss 150 66.3 American Eagle 147 66 Wildfire 155 66 Deja Vu 177 65.6 Batman Knight Flight 148 65 Hercules 151 65 Kraken 144 65 Mean Streak 155 65 Medusa 150 65 Orient Express 115 65 Rattler 124 65 Riddler's Revenge 146 65 Steel Eel 150 65 Texas Giant 137 65 Beast 141 64.8 Chang 144 63 Scream! 141 63 Tennessee Tornado 128 63

Colossus 115 62 Screamin' Eagle 92 62 Hangman 95 55 Hurricane 100 55 Invertigo 138 55 Iron Wolf 90 55 Kong 95 55 Mind Eraser 95 55 Silver Bullet 75 55 Starliner 76 55 T2 95 55 Thunderbolt 95 55 Timber Wolf 95 53 Wild One 88 53 Cheetah 90 52 Cannon Ball 70 50 Coaster Thrill Ride 52 50 Comet 78 50

The first 2-part question of your project will require you to use concepts learned in a z-test. This includes means were the population standard deviation is known and proportions. As usual, fill in the values in the colored boxes and write your conclusion in the space provided. Fill in the values from the question for "Data Entry" cells, a formula for "Formula" cells and a function (like =NORM.DIST) for "Function" cells. A. The board of a major credit card company requires that the mean wait time for customers when they call customer service is 2.75 minutes. To make sure that the mean wait time is not exceeding the requirement, an assistant manager tracks the wait times of 40 randomly selected calls. The mean wait time was calculated to be 3.01 minutes. Assuming the population standard deviation is 1.4 minutes, is there sufficient evidence that the mean wait time for customers is longer than 2.75 minutes with a 98% level of confidence? (7 points) B. For the same problem as part A, construct an appropriate confidence interval based on the alpha level in A to support your conclusion from part A. Recall, if you rejected the null in part A, then your expected mean should not be included in the interval. If you failed to reject the null hypothesis, then the hypothesized mean should be in the interval. You should only need the appropriate critical value and margin of error in addition to values from part A. Correctly round your results to two decimal places in your conclusion sentence and be sure to state that it supports your decision to reject or fail to reject based on whether the hypothesized value falls in the interval. (3 points)

1 pt A Null Hypothesis µ = 0 Data Entry 1 pt Alternative Hypothesis µ > 0 Alt Hyp (choose) 1 pt Sample Mean (x-bar) 27.9 Data Entry 3.4 Data Entry Sample Size (n) 11 Data Entry Degrees of Freedom (df) 10 Formula alpha-level 0.025 Data Entry 1 pt t-Score 2.8288858506 Formula 1 pt p-value 0.00894302354 Function 2 pts 1 pt B Critical Value 2.22813885199 Function Margin of Error 2.28415107997 Formula Confidence Interval 25.61584892 30.18415107997 (Lower Limit, Upper Limit) 2 pts Sample Standard Deviation (s) With p=0.0089 < a= 0.025, we Reject the null hypothesis. With 97.5% confidence, there is sufficient evidence to support the Alternative hypothesis, that Cox Communcations takes longer than 25 minutes to arrive. With 97.5% confidence, we can claim that the true arrival time falls between 25.62 minutes and 30.18 minutes. Since the hypothesized time of 25 minutes falls outside this interval this supports rejecting the null hypothesis T co d m A h te O lo su e m w B in A n th th p se to p

1 pt A Null Hypothesis (enter hypothesized diff) p1-p2 = 0 1 pt Alternative Hypothesis p1-p2 > 0 Proportion 1 x (Last Year's Data) 1500 Proportion 1 n (Last Year's Data) 2126 Proportion 1 p-hat 0.705550329 Proportion 2 x (This Year's Data) 1512 Proportion 2 n (This Year's Data) 2020 Proportion 2 p-hat 0.748514851 p-bar 0.726483357 1-(p-bar) 0.273516643 alpha-level 0.05 1 pt z-Score -3.102043898 1 pt p-value 0.999039053 2 pts 1 pt B Point Estimate -0.042964522 Critical Value 1.644853627 Margin of Error 0.022726769 Confidence Interval -0.065691292 (Formulas) Lower Limit 2 pts Inputs 1 pt With p= 0.999 > a = 0.05, we Fail to Reject the null hypothesis. This indicat insufficient evidence at the 0.05 level of signicicance to say that the changes be improved retention rates. With a 5% level of significance, we can say that the rate has decreased between 0 does not fall in this interval, this supports failing to reject the Null h

Data Entry Alt Hyp (choose) Data Entry Data Entry Formula Data Entry Data Entry Formula Formula Formula Data Entry Formula Function Formula Function Formula -0.02023775277278 Upper Limit tes that there is ellevue has made has n 6.6% and 2%. Since hypothesis. Yup. Another 2-part question. This time we are dealing with 2-samples. A. Officials at Bellevue University hope that changes they have made have improved the retention rate. Last year a sample of 2126 freshmen showed that 1500 returned as sophomores. This year 1512 of 2020 freshmen returned as sophomores. Determine if there is sufficient evidence at the 0.05 level to say that the retention rate has improved. (7 points) B. For the same problem as part A, construct an appropriate confidence interval based on the alpha level in A to support your conclusion from part A. Recall, if you rejected the null in part A, then your expected mean should not be included in the interval. If you failed to reject the null hypothesis, then the hypothesized mean should be in the interval. You should only need the appropriate critical value and margin of error in addition to values from part A. Correctly round your percentage to one decimal place in your conclusion sentence and be sure to state that it supports your decision to reject or fail to reject based on whether the hypothesized value falls in the interval. (3 points)

Paste your scatterplot with the regression equation and r-squared value below: For your last question on you. The data set in colu speed in mph and drop d this data, do the followin A. Create a scatterplot o title "Rollercoaster Spee be sure to add both axis B. Use the "Add chart el and r-squared value on y Keep in mind that you o one line of regression. If you will earn 0 points. 0 50 100 150 200 250 300 350 0 10 20 30 40 50 60 70 80 90 100 f(x) = 0.164066026489507 x + 42.0083816111709 R² = 0.786577490946543 Rollercoaster Speed (mph) vs. Drop Distance Drop Distance Speed (MPH)

n your last project, I am going to take it easy on umns A-C of the Data Set page give the name, top distance of several popular roller coasters. Using ng: of the data (4 pts). The scatterplot should have the ed vs. Drop Distance" (1 pts). Using the Design tab, s titles (1 pts) and a trendline (2 pts). lements" option to display both the LSRL equation your scatterplot. (2 points) only have one set of data, so you should only have f you submit a scatterplot with two separate lines,