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In an attempt to determine why customer service is important to managers in the US, researchers surveyed managing directors of manufacturing plants in Alaska. One of the reasons proposed was that customer service is a means of retaining customers. Om a scale of $1$ to $5$, with $14$ being low and $5$ being high, the survey respondents rated this reason more highly than any of the others, with a mean response of $4.30$. Suppose UK researchers believe British manufacturing managers would not rate this reason as highly and conduct a hypothesis test to prove their theory. Alpha is set at $0.05$. Data are gathered and the following results are obtained. Use these data to test whether UK managers rate this reason significantly lower than the $4.30$ mean ascertained in the US. What is the $p$-value of this test?

3 4 4

4 4 3

5 4 5

5 4 4

4 5 4

5 4 5

5 4 4

4 4 4

4 3 4

4 4 5

4 4

PS - Should I use the sampling theory formula? Help and thanks!

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Welcome to MSE! Please don't give us your homework to do and if it is homework, tag it as such. Tell us what you have tried and we will help you. –  Jeremy Mar 19 '13 at 18:52
Sorry and thanks! –  user59117 Mar 19 '13 at 19:42

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