b. What is the p-value for a sample of 100 undergraduate students with a sample mean credit card balance of $3,467? In a study entitled "How Undergraduate Students Use Credit Cards," Sallie Mae reported that undergraduate students have a mean credit card balance of $3194. This figure was an all-time high and had increased 49% over the previous five years. Assume that a current study is being conducted to determine if it can be concluded that the mean credit card balance for undergraduate students has continued to increase compared to the April 2009 report. Based on previous studies, use a population standard deviation $ \sigma = 1200 $.a. State the null and alternative hypotheses.\[ H_0 : \mu = 3194 \]\[ H_a : \mu > 3194 \]b. What is the *p*-value for a sample of 100 undergraduate students with a sample mean credit card balance of $3467? If your answer is zero enter "0."- $ z $ value (to 2 decimals): [ ]- *p*-value (to 4 decimals): [ ]c. Using a 0.01 level of significance, what is your conclusion?- [Select your answer] Conclude that student mean credit card debt is [Select your answer] than $3194.(Note: The image includes fields for answers to be entered and a "Check My Work" button to check the responses entered.)

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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b. What is the p-value for a sample of 100 undergraduate students with a sample mean credit card balance of $3,467?

In a study entitled "How Undergraduate Students Use Credit Cards," Sallie Mae reported that undergraduate students have a mean credit card balance of $3194. This figure was an all-time high and had increased 49% over the previous five years. Assume that a current study is being conducted to determine if it can be concluded that the mean credit card balance for undergraduate students has continued to increase compared to the April 2009 report. Based on previous studies, use a population standard deviation $ \sigma = 1200 $.

a. State the null and alternative hypotheses.

\[ H_0 : \mu = 3194 \]

\[ H_a : \mu > 3194 \]

b. What is the *p*-value for a sample of 100 undergraduate students with a sample mean credit card balance of $3467? If your answer is zero enter "0."

- $ z $ value (to 2 decimals): [ ]
- *p*-value (to 4 decimals): [ ]

c. Using a 0.01 level of significance, what is your conclusion?

- [Select your answer]

Conclude that student mean credit card debt is [Select your answer] than $3194.

(Note: The image includes fields for answers to be entered and a "Check My Work" button to check the responses entered.)

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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