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Finding Critical t Values When finding critical values, we often need significance levels other than those available in Table A-3. Some computer programs approximate critical t values by calculating
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- amu mun nuo 19. Commute Time to Work A survey of 15 large U.S. cities finds that the average commute time one way is 25.4 minutes. A chamber of commerce executive Technology Step by Step TI-84 Plus Hypothesis Test for the M 1. Enter the data values into L1. 2. Press STAT and move the c 3. Press 2 for T-Test. Step by Step 4. Move the cursor to Data and 5. Type in the appropriate valuarrow_forwardA paper gives data on x = change in Body Mass Index (BMI, in kilograms/meter) and y = change in a measure of depression for patients suffering from depression who participated in a pulmonary rehabilitation program. The table below contains a subset of the data given in the paper and are approximate values read from a scatterplot in the paper. BMI Change (kg/m²) -0.5 0.7 0.5 0.1 0.8 1 1.5 1.2 1 0.4 0.4 Depression Score Change -1 4 4 8 13 14 16 18 12 14 The accompanying computer output is from Minitab. Fitted Line Plot Depression score change = 6.598 + 5.327 BMI change 20- 5.10254 R-Sq R-Sq (adj) 20.06% 27.32% 15- 10- 5- 0- -0.5 0.0 0.5 1.0 1.5 BMI change R-sq 5.10254 27.32% Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 6.598 2.19 3.01 0.0132 BMI change 5.327 2.75 1.94 0.0812 1.00 Regression Equation Depression score change = 6.598 + 5.327 BMI change (a) What percentage of observed variation in depression score change can be explained by the simple linear regression model?…arrow_forward= The table available below shows the costs per mile (in cents) for a sample of automobiles. At α = 0.01, can you conclude that at least one mean cost per mile is different from the others? Click on the icon to view the data table. Let μss, HMS, HLS, Hsuv and μMy represent the mean costs per mile for small sedans, medium sedans, large sedans, SUV 4WDs, and minivans respectively. What are the hypotheses for this test? A. Ho: Hss HMS PLS SUV HMV H₂: Not all the means are equal. B. Ho: Hss HMS = μLS="SUV HMV Ha: Hss HMS HLS #μSUV HMV C. Ho: Not all the means are equal. Ha: ss = μms = μLS = μSUV="MV D. Ho: Hss #HMS # μLS #HSUV # HMV Ha: Hss HMS = μLS="SUV =HMV What is the test statistic? FSTAT= 32.33 (Round to two decimal places as needed.) What is the P-value? P-value= (Round to three decimal places as needed.)arrow_forward
- A paper gives data on x = change in Body Mass Index (BMI, in kilograms/meter2) and y = change in a measure of depression for patients suffering from depression who participated in a pulmonary rehabilitation program. The table below contains a subset of the data given in the paper and are approximate values read from a scatterplot in the paper. BMI Change (kg/m²) 0.5 -0.5 0 0.1 0.7 0.8 1 1.5 1.2 1 0.4 0.4 Depression Score Change -1 9 4 4 5 8 13 14 17 18 12 14 The accompanying computer output is from Minitab. Fitted Line Plot Depression score change = 6.512 + 5.472 BMI change 20 S 5.26270 R-Sq 27.16% R-Sq (adj) 19.88% 15- : 10- -0.5 0.0 1.5 Ⓡ S 5.26270 Coefficients Term Coef VIF SE Coef 2.26 T-Value 2.88 P-Value 0.0164 Constant 6.512 BMI change 5.472 2.83 1.93 0.0823 1.00 Regression Equation Depression score change = 6.512 + 5.472 BMI change (a) What percentage of observed variation in depression score change can be explained by the simple linear regression model? (Round your answer to…arrow_forwardOcean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents. x days 76 79 36 95 207 y km/100 14.2 19.6 5.4 11.2 35.9 (a) Verify that Σx = 493, Σy = 86.3, Σx2 = 65,187, Σy2 = 2029.21, Σxy = 11317.3, and r ≈ 0.93885. Σx Σy Σx2 Σy2 Σxy r (b) Use a 1% level of significance to test the claim ρ > 0. (Use 2 decimal places.) t critical t (c) Verify that Se ≈ 4.6183, a ≈ 0.5575, and b ≈ 0.1694. Se a b Find the predicted distance (km/100) when a drift bottle has been floating for 60 days. (Use 2…arrow_forwardOcean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents. 203 x days y km/100 72 76 32 14.7 94 11.7 19.5 5.3 35.6 (a) Verify that Ex = 477, Ey = 86.8, Ex? = 62,029, Ey2 = 2028.68, Exy = 11036.6, and r= 0.93853. Ex Ey Ex? Ey2| Exy (b) Use a 1% level of significance to test the claim p> 0. (Use 2 decimal places.) critical t Conclusion Reject the null hypothesis, there is sufficient evidence that p > 0. Reject the null hypothesis, there is insufficient evidence that p > 0. O Fail to reject the null hypothesis, there is insufficient evidence that p > 0. O…arrow_forward
- Select the correct answer below: r is significant because it is between the positive and negative critical values. r is not significant because it is between the positive and negative critical values. r is significant because it is not between the positive and negative critical values. r is not significant because it is not between the positive and negative critical values.arrow_forwardTwo manufacturing companies of soap each claims that their product is superior in whitening one’s complexion. A researcher did an experiment by randomly choosing two groups and assigning each group to use the product for one month. Results are shown below where the higher the number, the more effective the product in skin whitening. At (t-tabular value is ) level, is there a significant difference between the two products effectiveness in skin whitening? Product (Soap A or B) A 10 12 13 13 15 15 15 17 18 24 25 25 25 27 28 30 30 B 8 9 11 15 16 16 16 19 20 21 25 25 26 28 29 30 30 32 33 33arrow_forwarda sample of n=7 scores has the mean of M=16. One score in the population is changed from X=20 to X=5. What is the vaule of the new population mean?arrow_forward
- The critical value of chi-square is what when degrees of freedom equal 9 and a equals .05?arrow_forwardHELP WITH C AND PLEASE EXPLAIN HOW TO DO IT.arrow_forwardOcean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents. x days 75 79 35 91 203 y km/100 14.2 19.1 5.8 11.2 35.4 (a) Verify that Σx = 483, Σy = 85.7, Σx2 = 62,581, Σy2 = 1978.69, Σxy = 10982.3, and r ≈ 0.94895. Σx Σy Σx2 Σy2 Σxy r (b) Use a 1% level of significance to test the claim ρ > 0. (Use 2 decimal places.) t critical t (c) Verify that Se ≈ 4.1118, a ≈ 0.7378, and b ≈ 0.1698. Se a barrow_forward
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