Question

5. A company is researching the effectiveness of a new website design to decrease the time to access a website. Five website users were randomly selected and their times (in seconds) to access the website with the old and new designs were recorded. The results follow.

  

Let α = 0.05. Is the mean time to access the new website design shorter, or is (time for the old design - time for the new design) greater than zero? Express your answer in terms of the null hypothesis.

Answer 1

null hypothesis : - mean time to access the new website design is not shorter (time for the old design(1)  - time for the new design(2) is not greater than zero = 1 - 2    0

v/s

Alternative hypothesis :-mean time to access the new website design is not shorter (time for the old design(1)  - time for the new design(2) is not greater than zero = 1 - 2 > 0

t test

The Independent Samples t Test compares the means of two independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different.

The Independent Samples t Test is commonly used to test the following:

• Statistical differences between the means of two groups
• Statistical differences between the means of two interventions
• Statistical differences between the means of two change score

test statistic :-

  

find the calculated value and cheak it with table t value with df and alpha.( = 0.05)

Decision rule :-

if calculated t value > table t value reject the null hypothesis at level of significance ( = 0.05)

if calculated t value < table t value accept the null hypothesis at level of significance.( = 0.05)