At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $85 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $4.50. Over the first 47 days she was employed at the restaurant, the mean daily amount of her tips was $86.06. At the 0.01 significance level, can Ms. Brigden conclude that her daily tips average more than $85? |
a. | State the null hypothesis and the alternate hypothesis. | ||||||||
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b. | State the decision rule. | ||||||||
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c. | Compute the value of the test statistic. (Round your answer to 2 decimal places.) |
Value of the test statistic |
d. | What is your decision regarding H0? | ||||
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e. | What is the p-value? (Round your answer to 4 decimal places.) |
p-value |
Solution :
= 85
= 86.06
= 4.50
n = 47
a ) This is the right tailed test .
The null and alternative hypothesis is ,
H0 : ≤ 85
Ha : > 85
b
Test statistic = z
= ( - ) / / n
= (86.06- 85) /4.50 / 47
= 1.61
z = 1.61
b ) it is observed that z = 1.615 ≤ zc = 2.33, it is then concluded that the null hypothesis is not rejected
c ) Test statistic z is = 161
d ) Do not reject H0
e ) P(z >1.61) = 1 - P(z < 1.61 ) = 1 - 0.9463 = 0.0537
P-value = 0.0537
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