# Hypothesis testing, P-value and Z score

At the time he was hired as a server at the Family Restaurant, Bob was told, "You can average more than $20 a day in tips." Over the first 36 days he was employed at the restaurant, the mean daily amount of his tips was $24.85 with a standard deviation of $3.24. With a 1% (or .01) Level of Significance, can Bob conclude that he is probably earning more that $20 per day in tips?

a. Please state the null and alternative hypothesis in symbols and in words. (Hint: Ho: mu = $20 per day)

b. What is the z score calculated using the sample and population information? (Hint: When you don't have the population standard deviation you can substitute the SAMPLE standard deviation.)

c. What is the P-value (i.e. the area underneath the curve ABOVE the z-score calculated in part b)

d. Compare the P-value to the Level of Significance. Do you accept or reject Ho.

e. Answer the original question (Hint: don't forget to use the word "probably" in your answer to account for the level of significance.)

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#### Solution Summary

This solution answers various probability problems.