Question 1 > myOpenMath Background: Henry Cavendish carried out a series of experiments in 1798 to determine the mean density of the earth, as an indirect means to calculate the gravitational constant. A measurement of 5.5 indicates the earth's density is 5.5 times that of water. Source: Cavendish, H. (1798). Experiments to determine the density of the earth. Philosophical Transactions of the Royal Society of London, 88 (Part II), 469-527. Directions: Perform an appropriate significance test to determine whether or not Henry Cavendish's measurements for the density of the earth were different from the true value of 5.513. 1. Click on the Data button shown below to display the data and copy and paste it into a statistical software package. Click the Data button a second time to hide the data. Data Density 5.5 5.57 5.42 5.61 5.53 5.47 4.98 5.62 5.63 5.07 5.19 5.44 5.26 5.34 5.46 5.55 5.34 5.4 5.26 5.79 5.75 5.29 5.1 5.78 5.58 5.27 5.95 5.65 5.49 2. Use the statistical software package to compute a numerical summary. 3. Perform the significance test. a. Choose the correct null and alternative hypothesis. O Ho 5.513 H : < 5.513 O H : - = 5.513 H : > 5.513 O Ho 5.513 H : # 5.513 H : # 5.513 Ha = 5.513 b. Compute the test statistic. Round your answer to 4 decimal places. c. Compute the p-value. Round your answer to 4 decimal places. d. Interpret the results of the test. O The p-value provides little evidence against the null hypothesis. The difference between Henry Cavendish's measurements for the density of the earth and the true value are not statistically significant. O The p-value provides strong evidence against the null hypothesis. The difference between Henry Cavendish's measurements for the density of the earth and the true value are statistically significant. Question Help: Message instructor Submit Question Progress saved Done