Concept explainers
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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ELEMENTARY STATISTICS-MYLAB STAT.ACCESS
- Find the z-score corresponding to the given value and use the z-score to determine whether the value is significantly low or high. Consider a score to be significantly low if its z-score is less than or equal to -2. Consider a z-score to be significantly high if it is greater than or equal to 2. Round the z-score to the nearest tenth if necessary. A body temperature of 96.7° F given that human body temperatures have a mean of 98.20° F and a standard deviation of 0.62°.arrow_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 -0.5 0.1 0.7 0.8 1 1.5 1.2 1 0.4 0.4 Depression Score Change -1 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 5.26270 20- R-Sq R-Sq (adj) 19.88% 27.16% 15- 10- 5- 0- -0.5 0.0 0.5 1.0 1.5 BMI change R-są 5.26270 27.16% Coefficients Term Coef SE Coef T-Value P-Value VIF 6.512 5.472 Constant 2.26 2.88 0.0164 BMI change 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…arrow_forwardResearchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results given below are among the results obtained in the study. Higher scores correspond to greater pain levels. Is this study an experiment or an observational study? Explain. Reduction in Pain Level After Magnet Treatment: n = 20, x = 0.486, s = 0.964 Reduction in Pain Level After Sham Treatment: n = 20, x = 0.436, s = 1.44 ..... Choose the correct answer below. A. The study is an observational study because there was no attempt to modify the individuals being studied. B. The study is an experiment because the subjects are a systematic sample. C. The study is an experiment because subjects were given treatments. D. The study is an observational study because the subjects are a simple random sample.arrow_forward
- 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_forwardResearchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results given below are among the results obtained in the study. Higher scores correspond to greater pain levels. Is this study an experiment or an observational study? Explain. Reduction in Pain Level After Magnet Treatment: n= 20, x = 0.493, s= 0.957 Reduction in Pain Level After Sham Treatment: n = 20, x = 0.436, s= 1.42 Choose the correct answer below. O A. The study is an experiment because the subjects are a systematic sample. O B. The study is an observational study because there was no attempt to modify the individuals being studied. O c. The study is an experiment because subjects were given treatments. O D. The study is an observational study because the subjects are a simple random sample.arrow_forwardA chi-square test for independence is being used to evaluate the relationship between two variables, one of which is classified into 2 categories and the second of which is classified into 4 categories. What is the df value for the chi-square statistic? Group of answer choices df = 7 df = 6 df = 2 df = 3arrow_forward
- A 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_forwardA researcher wants to determine if there is a relationship between the number of hours spent by students on social media sites and self-esteem levels. A random sample of 10 statistics students was part of the study. Use manual calculations at α = 0.05 to calculate whether there is a significant relationship between the two variables. Show all your calculations.arrow_forwardA teacher gives a reading skills test to a third-grade class of n = 25 at the beginning of the school year. To evaluate the changes that occur during the year, students are tested again at the end of the year. Their test scores showed an average improvement of MD = 12.7 points with s2 = 100. Which variables are described in this scenario and what are their scales of measurement? Which test should you use?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_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) 0.7 0.8 1 1.5 1.2 1 0.4 0.4 0.5 -0.5 0.1 Depression Score Change -1 | 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 5.26270 20 - R-Sq R-Sq (adj) 19.88% 27.16% 15- 10-. 5- -0.5 0.0 0.5 1.0 1.5 BMI change 5.26270 27.166 Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 6.512 2.26 2.88 0.0164 BMI change 5.472 2.83 1.93 0.0823 1.00 Regression Equation Depression score change = 6.512 + 5.472 EMI change (a) What percentage of observed variation in depression score change can be explained by the simple linear regression model?…arrow_forwardThe data found below measure the amounts of greenhouse gas emissions from three types of vehicles. The measurements are in tons per year, expressed as CO2 equivalents. Use a 0.025significance level to test the claim that the different types of vehicle have the same mean amount of greenhouse gas emissions. Based on the results, does the type of vehicle appear to affect the amount of greenhouse gas emissions? Determine the test statistic. F= (Round to two decimal places as needed.) Identify the P-value. P-value= (Round to two decimal places as needed.) What is the conclusion of the test? the null hypothesis. Conclude that the type of vehicleappear to affect the amount of greenhouse gas emissions for these three types.arrow_forward
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