The loan manager for State Bank and Trust has claimed that the mean loan balance on outstanding loans at the bank is over $14,500.To test this at a significance level of 0.05,a random sample of n = 100 loan accounts is selected.Assuming that the population standard deviation is known to be $3,000,the null and alternative hypotheses to be tested are:
H₀ : μ ≤ $14,500
H_A : μ > $14,500

Question

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The null hypothesis (H₀) represents the status quo or the claim to be tested, which is that the mean loan balance is $14,500 or less. The alternative hypothesis (Hₐ) represents the claim that the mean loan balance is greater than $14,500, aligning with the loan manager's claim.

The Loan Manager for State Bank and Trust Has Claimed