## Testing the difference between two sample means-illustration, Mathematics

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An observation was made concerning reading abilities of males and females. The observation leads to a conclusion that females are faster readers than males. The observation was based upon the times taken by both males and females when reading out a list of names throughout graduation ceremonies.

In order to investigate into the observation and the consequent conclusion a sample of 200 men were described lists to read. On average each man took 63 seconds along with a standard deviation of 4 seconds

A sample of 250 women were taken and asked also to read the similar list of names. This was found that they on average took 62 seconds along with a standard deviation of 1 second.

Required

By conducting a statistical hypothesis testing at 1 level of significance establish whether the sample data obtained does support earlier observation or not

Solution

H0: µ1 = µ2

H1: µ1 ≠ µ2

Critical values of the two tailed test is at 1 percent level of significance is 2.58.

Z = (x¯1 - 2)/S(x¯1 - 2)

Z = ¦ {(63 - 62)/√ ((42/200) + (12/250))} ¦

= 3.45 As 3.45 > 2.33 reject the null hypothesis but accept the alternative hypothesis at 1 percent level of significance that is there is a significant difference among the reading speed of females and males, thus females are actually faster readers.

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