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. Open the data set: Click on the Data button shown below to display the data in a single column. This makes it easier to copy the data into a statistical software package. Then click the Data button a second time to hide the data. Data Density 5.5 5.57 5.32 5.61 5.53 5.47 4.88 5.62 5.63 5.17 5.19 5.34 5.36 5.44 5.36 5.55 5.24 5.3 5.36 5.79 5.75 5.29 5.1 5.68 5.58 5.27 5.85 5.55 5.39 Compute a numerical summary: Use a statistical software package to determine the sample size and compute the sample mean and standard deviation. Significance test. 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. a. State the null and alternative hypothesis. OHo5.513 Ha 5.513 OHo5.513 Ha >5.513 f OHo5.513 Ha 5.513 OHo5.513 Ha 5.513 b. Compute the test statistic. (Round you answer to 4 decimal places) c. Compute the p-value. (Round you answer to 4 decimal places) d. Interpret the results of the test. 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. 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.
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. Open the data set: Click on the Data button shown below to display the data in a single column. This makes it easier to copy the data into a statistical software package. Then click the Data button a second time to hide the data. Data Density 5.5 5.57 5.32 5.61 5.53 5.47 4.88 5.62 5.63 5.17 5.19 5.34 5.36 5.44 5.36 5.55 5.24 5.3 5.36 5.79 5.75 5.29 5.1 5.68 5.58 5.27 5.85 5.55 5.39 Compute a numerical summary: Use a statistical software package to determine the sample size and compute the sample mean and standard deviation. Significance test. 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. a. State the null and alternative hypothesis. OHo5.513 Ha 5.513 OHo5.513 Ha >5.513 f OHo5.513 Ha 5.513 OHo5.513 Ha 5.513 b. Compute the test statistic. (Round you answer to 4 decimal places) c. Compute the p-value. (Round you answer to 4 decimal places) d. Interpret the results of the test. 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. 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.
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Author:Bruce Crauder, Benny Evans, Alan Noell
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Transcribed Image Text: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.
Open the data set: Click on the Data button shown below to display the data
in a single column. This makes it easier to copy the data into a statistical
software package. Then click the Data button a second time to hide the data.
Data
Density
5.5
5.57
5.32
5.61
5.53
5.47
4.88
5.62
5.63
5.17
5.19
5.34
5.36
5.44
5.36
5.55
5.24
5.3
5.36
5.79
5.75
5.29
5.1
5.68
5.58
5.27
5.85
5.55
5.39
Compute a numerical summary: Use a statistical software package to determine the sample size and
compute the sample mean and standard deviation.
Significance test. 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.
a. State the null and alternative hypothesis.
OHo5.513
Ha 5.513
OHo5.513
Ha: 5.513
OHo5.513
H₁ < 5.513
OHo5.513
H₁: = 5.513
b. Compute the test statistic. (Round you answer to 4 decimal places)
c. Compute the p-value. (Round you 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.
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