10.50The sample mean is $4.54, the sample standard deviation is $1.35 ## Text Transcription for Educational Website### 10.4 Hypothesis Tests for a Population Mean#### Page 491**10.49** The report "Highest Paying Jobs for 2009–10 Bachelor's Degree Graduates" (National Association of Colleges and Employers, February 2010) states that the mean yearly salary offer for students graduating with a degree in accounting in 2010 is $48,722. Suppose that a random sample of 50 accounting graduates at a large university who received job offers resulted in a mean offer of $49,850 and a standard deviation of $3300. Do the sample data provide strong support for the claim that the mean salary offer for accounting graduates of this university is higher than the 2010 national average of $48,722? Test the relevant hypotheses using $ \alpha = 0.05 $.**10.50** _The Economist_ collects data each year on the price of a Big Mac in various countries around the world. The price of a Big Mac for a sample of McDonald's restaurants in Europe in May 2009 resulted in the following Big Mac prices (after conversion to U.S. dollars): 3.80, 5.89, 4.92, 3.88, 2.65, 5.57, 6.39, 3.24The mean price of a Big Mac in the U.S. in May 2009 was $3.57. For purposes of this exercise, assume it is reasonable to regard the sample as representative of European McDonald's restaurants. Does the sample provide convincing evidence that the mean May 2009 price of a Big Mac in Europe is greater than the reported U.S. price? Test the relevant hypotheses using $ \alpha = 0.05 $.**10.51** A credit bureau analysis of undergraduate students' credit records found that the average number of credit cards in an undergraduate’s wallet was 4.09 ("Undergraduate Students and Credit Cards in 2004," Nellie Mae, May 2005). It was also reported that in a random sample of 132 undergraduates, the sample mean number of credit cards that the students said they carried was 3.50. The sample standard deviation was not reported. Suppose that it [...](Note: The text for 10.51 appears to be incomplete in the image provided.)

Name: 10.50The sample mean is $4.54, the sample standard deviation is $1.35
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Description: 10.50The sample mean is $4.54, the sample standard deviation is $1.35 ## Text Transcription for Educational Website### 10.4 Hypothesis Tests for a Population Mean#### Page 491**10.49** The report "Highest Paying Jobs for 2009–10 Bachelor's Degree Gr

Answered: O The Economist collects data each year…

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10.50

The sample mean is $4.54, the sample standard deviation is $1.35

## Text Transcription for Educational Website

### 10.4 Hypothesis Tests for a Population Mean

#### Page 491

**10.49**
The report "Highest Paying Jobs for 2009–10 Bachelor's Degree Graduates" (National Association of Colleges and Employers, February 2010) states that the mean yearly salary offer for students graduating with a degree in accounting in 2010 is $48,722. Suppose that a random sample of 50 accounting graduates at a large university who received job offers resulted in a mean offer of $49,850 and a standard deviation of $3300. Do the sample data provide strong support for the claim that the mean salary offer for accounting graduates of this university is higher than the 2010 national average of $48,722? Test the relevant hypotheses using $ \alpha = 0.05 $.

**10.50**
_The Economist_ collects data each year on the price of a Big Mac in various countries around the world. The price of a Big Mac for a sample of McDonald's restaurants in Europe in May 2009 resulted in the following Big Mac prices (after conversion to U.S. dollars):
3.80, 5.89, 4.92, 3.88, 2.65, 5.57, 6.39, 3.24

The mean price of a Big Mac in the U.S. in May 2009 was $3.57. For purposes of this exercise, assume it is reasonable to regard the sample as representative of European McDonald's restaurants. Does the sample provide convincing evidence that the mean May 2009 price of a Big Mac in Europe is greater than the reported U.S. price? Test the relevant hypotheses using $ \alpha = 0.05 $.

**10.51**
A credit bureau analysis of undergraduate students' credit records found that the average number of credit cards in an undergraduate’s wallet was 4.09 ("Undergraduate Students and Credit Cards in 2004," Nellie Mae, May 2005). It was also reported that in a random sample of 132 undergraduates, the sample mean number of credit cards that the students said they carried was 3.50. The sample standard deviation was not reported. Suppose that it [...]

(Note: The text for 10.51 appears to be incomplete in the image provided.)

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 + ...

Expert Solution

Step 1

Null Hypothesis:

H0: There is no sample evidence that the mean price of a Big Mac in Europe is greater than $3.57.

Alternative Hypothesis:

H1: There is a sample evidence that the mean price of a Big Mac in Europe is greater than $3.57.

Test statistic:

Given,

$\bar{x} = 4.54 s = 1.35 n = 8 μ = 3.57$

$t = \frac{\bar{x} - μ}{\frac{s}{\sqrt{n}}} = \frac{4.54 - 3.57}{\frac{1.35}{\sqrt{8}}} = 2.0323$

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