1. The sufficiency of an electric toothbrush is often measured in terms of the r
ID: 3054794 • Letter: 1
Question
1. The sufficiency of an electric toothbrush is often measured in terms of the rotation speed, in revolutions per minute (rpm). Two brands were selected for comparison, and independent random samples of the electric toothbrush of each brand were obtained. The rotation speed for each brand was measured, and the summary is given below. Brand Type Sample Size Sample Mean Population Variance 23 25 7992 7988 460 2000 Construct the 95% two-sided confidence interval for the mean speed difference. a. b. Do the two brand types of electric toothbrush appear to have different rotation speeds, on average? If yes, then what brand type is better?Explanation / Answer
a)
t value at 95% = 2.0117
CI= (x1 -x2) +/- t * sqrt(s1^2/n1 +s2^2/n2)
= ( 7992 - 7988) + /- 2.0117
* sqrt(21.4476^2 /23 + 44.7214^2/25)
= (-16.1170 , 24.1170)
The 95% CI is (-16.1170 , 24.1170)
b)
As 0 is included in the CI there is no difference in the rotation speed of 2 different electronic toothbrushes .
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