Question

Example 1: A credit card company claims that the mean credit card debt for individuals is greater than $5,300. You want to test this claim. You find that a random sample of 27 cardholders has a mean credit card balance of $5,560 and a standard deviation of $575. At α = 0.05​, can you support the​ claim? Assume the population is normally distributed.

Write out the hypothesis statements below and identify the parameter of interest.

H_o: _________________________        

H_a: _________________________        

Which hypothesis represents the claim?   Circle one:   Null Hypothesis (H₀) or   Alternative Hypothesis (H_a)

Explain what type of hypothesis testing you will perform and whether conditions are met. one sample z-test          one sample t-test          one proportion z-test

Test this hypothesis. (SHOW WORK!) REJECTION REGION METHOD Clearly label a sketch with appropriate shading and calculate the test statistic (show formula and work). Find the critical value(s): _____________ Sketch and identify the rejection regions: Find the standardized test statistic: _________ Would you reject or fail to reject the null hypothesis? Circle one: Reject H0or Fail to Reject H0 Explain your choice:

Write a conclusion in the context of this problem.

Answer 1

The claim is alternative hypothesis.

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It is given that population is normally distributed and population standard deviation is unknown so t test will be used.

Correct option is one sample t-test.

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Following is the graph shows the critical region:

Conclusion:

There is evidence to support the credit card company claims that the mean credit card debt for individuals is greater than $5,300.