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# hypothesis testing for two means using two paired samples t test

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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:

User Old Website Design New Website Design
A 30 15
B 45 20
C 25 10
D 32 25
E 28 20

Let α = 0.10. 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?

a) What is the null hypothesis?

b) What is the alternate hypothesis

c) What is the dregree of freedom 8

d) What is the critical t value at 1% significance level: .10

e) Assume calculated t to be 2.70, at the .01 significance, what would be your decision

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