A credit card company claims that the mean credit đebt for individuals is greater 5,100. wani t this claim. You find that a random sample of 36 cardholders has a mean credit card balan $650. At a = 0.05, can you support the claim? Complete parts (a) through (e) below. Assume the population is normally distributed. a) Write the claim mathematically and identify Ho and Ha- Which of the following correctly states H, and H? VA. Ho: us $5,100 H:u> $5,100 O B. Ho: u> $5,100 O C. Họ: u= $5,100 Hgiu# $5,100 OF. Ho: u> $5,100 Hius $5,100 Hai us $5,100 O D. Ho: u= $5,100 H:u> $5,100 O E. Ho: u2 $5,100 H:u< $5,100 b) Find the critical value(s) and identify the rejection region(s). What is(are) the critical yalue(s), to?

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A credit card company claims that the mean credit card debt for individuals is greater than $5,100. You want to test this claim. You find that a random sample of 36 cardholders has a mean credit card balance of $5,271 and a standard deviation of $650. At α = 0.05, can you support the claim? Complete parts (a) through (e) below. Assume the population is normally distributed.

(a) Write the claim mathematically and identify \( H_0 \) and \( H_a \).

Which of the following correctly states \( H_0 \) and \( H_a \)?

- A: \( H_0: \mu \leq \$5,100 \)
  
  \( H_a: \mu > \$5,100 \) (Correct Choice)
  
- B: \( H_0: \mu > \$5,100 \)
  
  \( H_a: \mu \leq \$5,100 \)
  
- C: \( H_0: \mu = \$5,100 \)
  
  \( H_a: \mu \neq \$5,100 \)
  
- D: \( H_0: \mu = \$5,100 \)
  
  \( H_a: \mu > \$5,100 \)
  
- E: \( H_0: \mu = \$5,100 \)
  
  \( H_a: \mu < \$5,100 \)
  
- F: \( H_0: \mu \geq \$5,100 \)
  
  \( H_a: \mu < \$5,100 \)

(b) Find the critical value(s) and identify the rejection region(s).

What is(are) the critical value(s), \( t_0 \)?

\( t_0 = 1.690 \)

(Use a comma to separate answers as needed. Round to three decimal places as needed.)

Determine the rejection region(s). Select the correct choice below and fill in the answer box(es) within your choice. (Round to three decimal places as needed.)

- A: \( t < \square \)
- B: \( t < \square \) and \( t > \square \)
- C: \( t < t_0 \)
- D: \( t > \square \)

Explanation for graphs or diagrams: There is no graph or diagram in the image.
Transcribed Image Text:A credit card company claims that the mean credit card debt for individuals is greater than $5,100. You want to test this claim. You find that a random sample of 36 cardholders has a mean credit card balance of $5,271 and a standard deviation of $650. At α = 0.05, can you support the claim? Complete parts (a) through (e) below. Assume the population is normally distributed. (a) Write the claim mathematically and identify \( H_0 \) and \( H_a \). Which of the following correctly states \( H_0 \) and \( H_a \)? - A: \( H_0: \mu \leq \$5,100 \) \( H_a: \mu > \$5,100 \) (Correct Choice) - B: \( H_0: \mu > \$5,100 \) \( H_a: \mu \leq \$5,100 \) - C: \( H_0: \mu = \$5,100 \) \( H_a: \mu \neq \$5,100 \) - D: \( H_0: \mu = \$5,100 \) \( H_a: \mu > \$5,100 \) - E: \( H_0: \mu = \$5,100 \) \( H_a: \mu < \$5,100 \) - F: \( H_0: \mu \geq \$5,100 \) \( H_a: \mu < \$5,100 \) (b) Find the critical value(s) and identify the rejection region(s). What is(are) the critical value(s), \( t_0 \)? \( t_0 = 1.690 \) (Use a comma to separate answers as needed. Round to three decimal places as needed.) Determine the rejection region(s). Select the correct choice below and fill in the answer box(es) within your choice. (Round to three decimal places as needed.) - A: \( t < \square \) - B: \( t < \square \) and \( t > \square \) - C: \( t < t_0 \) - D: \( t > \square \) Explanation for graphs or diagrams: There is no graph or diagram in the image.
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