The development engineer of a company making razors has been asked by the marketing department to compare the shaving times of the company's standard razor and deluxe razor. The development engineer records the time, X, it takes him to shave, on seven mornings, using a standard razor. The times, in seconds, were:
217, 210, 254, 237, 232, 228, 243
His assistant volunteers to test the deluxe razor over six mornings and produces the following times, Y, measured in seconds:
186, 219, 168, 202, 191, 184
(i) Determine the sample mean and standard deviation for Sample X and Sample Y.
(ii) Determine a 95 per cent confidence interval of the difference between the two means.
(iii) Does this confidence interval suggest that there is a difference between the two shaving times? Explain.
(iv) Comment on the design of this study.