Question

1. Determine if the following statement is true or false. If the statement is​ false, give a brief explanation.

The removal of an outlier with z=3.83 causes both the mean and the standard deviation of the data to decrease.

Choose the correct answer below.

A. The statement is true.

B. The statement is false because both the mean and the standard deviation of the data will stay the same because both the mean and the standard deviation are resistant to the effect of an outlier and will not change with its removal.

C. The statement is false because both the mean and the standard deviation of the data will increase because outliers pull the mean and inflate the standard deviation.

2. Suppose the mean time sales representatives spend on the road averages 45 hours per week with standard deviation 5.

a) Would it be surprising to meet a representative who spent 51 hours on the road last​ week?

b) Do you need to make any​ assumptions?

Answer 1

1) option A is right

The standard score of Z is equal to 3.83 depicts that the outlier is 3.83 standard deviation above the mean which means if we remove the outlier the total sum of the data decreases significantly. The divisor also get reduced by 1 similarly the standard deviation also get reduced when outlier is removed is there will be less variability in the data set

2) here the mean and the standard deviation are

A) We will convert this 51 hours to standard Z score

Thus 51 is 1.2 standard deviation (less than 2 standard deviation) above the mean which is not unusual. Hence

It would not be surprising to meet a representative who spent 51 hours on road last week

B) we have assumed that the distribution is normally distributed.