# Alternative Hypothesis on Credit Card Benefits

Not what you're looking for?

The Thompson's Discount Appliance Store issues its own credit card. The credit manager wants to find whether the mean monthly unpaid balance is more than $400...

(see attachment for full question)

The Thompson's Discount Appliance Store issues its own credit card. The credit manager wants to find whether the mean monthly unpaid balance

is more than $400. The level of significance is set at .05. A random check of 172 unpaid balances revealed the sample mean is $407 and the standard deviation of the sample is $38. Should the credit manager conclude the population mean is greater than $400, or is it reasonable that the difference of $7 ($407 - $400 =$7) is due to chance? ?

The null hypothesis Ho: the mean monthly unpaid balance is equal to $400.00.

The alternative hypothesis Ha: the mean monthly unpaid balance is more than $400.00.

Critical value z(.05)=1.645, rejection region is z > 1.645.

z-score is z=sqrt(172)*(407-400)/38=2.416.

2.416 > 1.645, we should reject Ho, thus the mean monthly unpaid balance is more than $400.00 at the level of .05.

It is unreasonable that the difference of $7.00 ($407-$400 = $7) is due to chance.

##### Purchase this Solution

##### Solution Summary

The Thompson's Discount Appliance Store issues its own credit card. The credit manager wants to find whether the mean monthly unpaid balance is more than $400. The level of significance is set at .05. A random check of 172 unpaid balances revealed the sample mean is $407 and the standard deviation of the sample is $38. Should the credit manager conclude the population mean is greater than $400, or is it reasonable that the difference of $7 ($407 - $400 =$7) is due to chance? ?

The null hypothesis Ho: the mean monthly unpaid balance is equal to $400.00.

The alternative hypothesis Ha: the mean monthly unpaid balance is more than $400.00.

Crutical value z(.05)=1.645, rejection region is z > 1.645.

z-score is z=sqrt(172)*(407-400)/38=2.416.

2.416 > 1.645, we should reject Ho, thus the mean monthly unpaid balance is more than $400.00 at the level of .05.

It is unreasonable that the difference of $7.00 ($407-$400 = $7) is due to chance.

##### Solution Preview

The detailed explanation of the solution is attached I included the explanation of how to apply the Central Limit Theorem (if necessary), the verbal and graphical explanation of the decision rule.

The Thompson's Discount Appliance Store issues its own credit card. The credit manager wants to find whether the mean monthly unpaid balance

is more than $400. The level of significance is set at .05. A random check of 172 unpaid balances revealed the sample mean is $407 and the standard deviation of the sample is $38. ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

##### Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

##### Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

##### Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.