A certified mechanic was timed for the repair of an automobile on 14 separate occasions. Over the same period, a trainee mechanic was timed for the repair of a similar automobile. The times in minutes are given below Certified 344 276 257 334 267 164 222 343 212 175 211 311 209 188 Trainee 222 342 178 234 398 232 377 211 309 190 351 343 177 269 a. Calculate a 99% confidence interval for the mean time taken to repair the automobile by the (i) certified mechanic and (ii) the trainee mechanic. b. Test the hypothesis that the two mean times for both mechanics are equal. Use the 5% level of significance. c. Subsequently, it was learned that the times for the trainee were incorrectly recorded and that each of the values above is 30 minutes too small. What, if any, the difference does this make to the results of the test done in part (d)?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A certified mechanic was timed for the repair of an automobile on 14 separate occasions.
Over the same period, a trainee mechanic was timed for the repair of a similar automobile.
The times in minutes are given below
Certified 344 276 257 334 267 164 222 343 212 175 211 311 209 188
Trainee 222 342 178 234 398 232 377 211 309 190 351 343 177 269
a. Calculate a 99% confidence interval for the
(i) certified mechanic and (ii) the trainee mechanic.
b. Test the hypothesis that the two mean times for both mechanics are equal. Use the 5% level of significance.
c. Subsequently, it was learned that the times for the trainee were incorrectly recorded and that each of the values above is 30 minutes too small. What, if any, the difference does this make to the results of the test done in part (d)?
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