A popular experiment in physics classes is to estimate the acceleration due to gravity, g, for example using pendulums or ticker-tape machines. The accepted value of g is 9.81 ms−2

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A student runs an experiment to estimate g ten times and gets the estimates 9.62 9.75 9.86 9.58 9.85 9.82 9.83 10.03 9.57 10.06

a. You can enter data vectors into R using the c() command.

For example, a data vector called gdat containing the first three numbers would be entered as gdat = c(9.62, 9.75, 9.86)

Enter the data into R and calculate the sample mean and standard deviation.

b. Decide upon suitable hypotheses to test the accuracy of the experimental results. Test the hypotheses using direct calculation of the test statistic, and interpret the results.

c. Based on the experimental data, construct an approximate 95% confidence interval for the gravitational acceleration constant.

d. Give the R command to repeat the test and confidence interval using the inbuilt t.test command. Verify that it gives the same results as you computed manually.