The average McDonald's restaurant generates $3.1 million in sales each year with a standard deviation of 0.4. Micah wants to know if the average sales generated by McDonald's restaurants in Maryland is different than the worldwide average. He surveys 19 restaurants in Maryland and finds the following data (in millions of dollars): 2.8, 3.2, 3.8, 4.2, 3.5, 3.2, 3.6, 3.2, 2.7, 3.1, 2.5, 3.2, 3.7, 3.5, 3.9, 3.9, 2.5, 2.9, 2.8 Perform a hypothesis test using a 9% level of significance. Step 1: State the null and alternative hypotheses. H0:H0: Ha:Ha: (So we will be performing a test.) Step 2: Assuming the null hypothesis is true, determine the features of the distribution of point estimates using the Central Limit Theorem. By the Central Limit Theorem, we know that the point estimates are with distribution mean and distribution standard deviation . Step 3: Find the pp-value of the point estimate. P(P( )=P()=P( )=)= pp-value== Step 4: Make a Conclusion About the null hypothesis. Since the pp-value== =α=α, we the null hypothesis. We cannot conclude that the mean sales of McDonald's restaurants in Maryland differ from average McDonald's sales worldwide. We conclude that the mean sales of McDonald's restaurants in Maryland differ from average McDonald's sales worldwide.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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The average McDonald's restaurant generates $3.1 million in sales each year with a standard deviation of 0.4. Micah wants to know if the average sales generated by McDonald's restaurants in Maryland is different than the worldwide average. He surveys 19 restaurants in Maryland and finds the following data (in millions of dollars):

2.8, 3.2, 3.8, 4.2, 3.5, 3.2, 3.6, 3.2, 2.7, 3.1, 2.5, 3.2, 3.7, 3.5, 3.9, 3.9, 2.5, 2.9, 2.8

Perform a hypothesis test using a 9% level of significance.

Step 1: State the null and alternative hypotheses.

H0:H0:
Ha:Ha:

(So we will be performing a      test.)

Step 2: Assuming the null hypothesis is true, determine the features of the distribution of point estimates using the Central Limit Theorem.

By the Central Limit Theorem, we know that the point estimates are     with distribution mean  and distribution standard deviation .

Step 3: Find the pp-value of the point estimate.

P(P(        )=P()=P(        )=)=

pp-value==

Step 4: Make a Conclusion About the null hypothesis.

Since the pp-value==     =α=α, we     the null hypothesis.

We cannot conclude that the mean sales of McDonald's restaurants in Maryland differ from average McDonald's sales worldwide.
We conclude that the mean sales of McDonald's restaurants in Maryland differ from average McDonald's sales worldwide.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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