Consider the data displayed below on the lifetimes of a sample of 10 laptop batt

Question

Consider the data displayed below on the lifetimes of a sample of 10 laptop batteries (in hours) from the same manufacturer. Suppose we want to investigate whether there is convincing evidence that the distribution of all battery lifetimes is skewed to the right. One possible statistic for measuring skewness is the ratio: (sample mean division sample median) (a) Calculate the value of this statistic (sample mean divided by the sample median) for this sample. (b) If the distribution of battery lifetimes in the population is symmetric, then we would expect the skewness ratio statistic to be: (choose ONE and fill in a number) i. LESS THAN ______________ ii. CLOSE TO ______________ iii. GREATER THAN ______________ (c) If the distribution of battery lifetimes in the population is skewed to the right, then we would expect the skewness ratio statistic to be: (choose ONE and fill in a number) i. LESS THAN ______________ ii. CLOSE TO ______________ iii, GREATER THAN ______________

Explanation / Answer

a) Value of statistic

= Mean / Median

= 2.600 / 2.475

= 1.05

b) In case of a symmetric distribution, Mean = Median

So in this scenario,

We would expect the skewness ratio statistic to be close to 1.

c) In case of a skewed right distribution, Mean > Median

So in this scenario,

We would expect the skewness ratio statistic to be greater than 1.

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