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At the time she was hired as a server at the Grumney Family restaurant, Beth Brigden...

At the time she was hired as a server at the Grumney Family restaurant, Beth Brigden was told, “You can average $80 a day in Tips”. Assume that the population of daily tips is normally distributed with a standard deviation of $3.24. Over the first 35 days she was employed at the restaurant, the mean daily amount of her tips was $84.85. At the 0.01 level of significance, can Ms. Brigden conclude that her daily tips average more than $80? Answer all the following:                                                                                                        

     a. Show your null and alternate hypotheses

     b. What is the value of the test statistic?

     c. What is the decision rule?

     d. What is your decision regarding your null hypothesis using the critical value method?

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

a)

H0: = 80

Ha: > 80

b)

Test statistics

z = - / ( / sqrt(n) )

= 84.85 - 80 / (3.24 / sqrt(35) )

= 8.86

c)

z critical value at 0.01 level = 2.326

Decision rule = Reject H0, if test statistics > 2.326

d)

Since test statistics falls in rejection region , we have sufficient evidence to reject H0

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