The waiters at a particular restaurant are trying to deduce the best strategies for increasing the tips they receive. They noticed that when they introduced themselves to the customers by name, the tips seemed to be higher. The following data gives information on the tip the waiters received (as a per- centage of the bill) both when they introduced themselves by name, and when they did not. Introduced with name: Not introduced with name: T = 22.59 S1 = 7.82 т — = 50 п 3D 50 = 14.14 S2 6.09 We want to run a hypothesis test to determine if this data provides compelling evidence that an introduction with their name increases tips on average by more than 50%. (a) State the relevant hypotheses for this test. [Hint: You will need to modify the usual 2-sample tests we have done in class. For this problem, consider hypotheses involving the parameter 0 = µ1 – 1.5µ2.] (b) Derive an appropriate test statistic to test the hypotheses from part (a). [Hint: Note that the sample sizes are large, so this will be some sort of z-test. To construct this test statistic, you will need to choose an estimator for 0, and calculate the standard deviation of this estimator for the denominator of the test statistic.] (c) Compute the p-value using your test statistic from part (b). = .05 significance. Is there compelling evidence that the (d) State your conclusion to the test at a average tip increases by 50% when the waiters introduce themselves by name?
The waiters at a particular restaurant are trying to deduce the best strategies for increasing the tips they receive. They noticed that when they introduced themselves to the customers by name, the tips seemed to be higher. The following data gives information on the tip the waiters received (as a per- centage of the bill) both when they introduced themselves by name, and when they did not. Introduced with name: Not introduced with name: T = 22.59 S1 = 7.82 т — = 50 п 3D 50 = 14.14 S2 6.09 We want to run a hypothesis test to determine if this data provides compelling evidence that an introduction with their name increases tips on average by more than 50%. (a) State the relevant hypotheses for this test. [Hint: You will need to modify the usual 2-sample tests we have done in class. For this problem, consider hypotheses involving the parameter 0 = µ1 – 1.5µ2.] (b) Derive an appropriate test statistic to test the hypotheses from part (a). [Hint: Note that the sample sizes are large, so this will be some sort of z-test. To construct this test statistic, you will need to choose an estimator for 0, and calculate the standard deviation of this estimator for the denominator of the test statistic.] (c) Compute the p-value using your test statistic from part (b). = .05 significance. Is there compelling evidence that the (d) State your conclusion to the test at a average tip increases by 50% when the waiters introduce themselves by name?
Chapter4: Linear Functions
Section4.3: Fitting Linear Models To Data
Problem 34SE: For the following exercises, consider this scenario: The profit of a company decreased steadily...
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![The waiters at a particular restaurant are trying to deduce the best strategies for increasing the tips
they receive. They noticed that when they introduced themselves to the customers by name, the tips
seemed to be higher. The following data gives information on the tip the waiters received (as a per-
centage of the bill) both when they introduced themselves by name, and when they did not.
Introduced with name:
Not introduced with name:
T = 22.59
S1 = 7.82
т —
= 50
п 3D 50
= 14.14
S2
6.09
We want to run a hypothesis test to determine if this data provides compelling evidence that an
introduction with their name increases tips on average by more than 50%.
(a) State the relevant hypotheses for this test. [Hint: You will need to modify the usual 2-sample
tests we have done in class. For this problem, consider hypotheses involving the parameter
0 = µ1 – 1.5µ2.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7808e20a-24a2-455e-a2e2-815bef479748%2F6a0e9729-6a1c-4497-840d-bed70722ff1e%2Fxsllaxk.png&w=3840&q=75)
Transcribed Image Text:The waiters at a particular restaurant are trying to deduce the best strategies for increasing the tips
they receive. They noticed that when they introduced themselves to the customers by name, the tips
seemed to be higher. The following data gives information on the tip the waiters received (as a per-
centage of the bill) both when they introduced themselves by name, and when they did not.
Introduced with name:
Not introduced with name:
T = 22.59
S1 = 7.82
т —
= 50
п 3D 50
= 14.14
S2
6.09
We want to run a hypothesis test to determine if this data provides compelling evidence that an
introduction with their name increases tips on average by more than 50%.
(a) State the relevant hypotheses for this test. [Hint: You will need to modify the usual 2-sample
tests we have done in class. For this problem, consider hypotheses involving the parameter
0 = µ1 – 1.5µ2.]
![(b) Derive an appropriate test statistic to test the hypotheses from part (a). [Hint: Note that the
sample sizes are large, so this will be some sort of z-test. To construct this test statistic, you will
need to choose an estimator for 0, and calculate the standard deviation of this estimator for the
denominator of the test statistic.]
(c) Compute the p-value using your test statistic from part (b).
= .05 significance. Is there compelling evidence that the
(d) State your conclusion to the test at a
average tip increases by 50% when the waiters introduce themselves by name?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7808e20a-24a2-455e-a2e2-815bef479748%2F6a0e9729-6a1c-4497-840d-bed70722ff1e%2F8fj7rgr.png&w=3840&q=75)
Transcribed Image Text:(b) Derive an appropriate test statistic to test the hypotheses from part (a). [Hint: Note that the
sample sizes are large, so this will be some sort of z-test. To construct this test statistic, you will
need to choose an estimator for 0, and calculate the standard deviation of this estimator for the
denominator of the test statistic.]
(c) Compute the p-value using your test statistic from part (b).
= .05 significance. Is there compelling evidence that the
(d) State your conclusion to the test at a
average tip increases by 50% when the waiters introduce themselves by name?
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