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
H_{0}: µ_{1} = µ_{2}
H_{1}: µ_{1} ≠ µ_{2}
Critical values of the two tailed test is at 1 percent level of significance is 2.58.
Z = (x¯_{1 }-_{ }x¯_{2})/S(x¯_{1 }-_{ }x¯_{2})
Z = ¦ {(63 - 62)/√ ((4^{2}/200) + (1^{2}/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.