an auditor wishes to test the assumption that the mean value of all accounts receivable in a given firm is $260.00 she will reject this claim only if it is clearly contradicted by the sample mean. the sample standard deviation of 36 accounts is $43, the sample mean is $250, and the level of significance is 5%

1. write out the null and alternative hypotheses.

2. Calculate the A test statistic.

3. Find the p-value.

1. The null hypothesis, denoted as H0, states that the mean value of all accounts receivable in the given firm is $260.00. The alternative hypothesis, denoted as Ha, is the opposite of the null hypothesis and states that the mean value of all accounts receivable in the given firm is not equal to $260.00.

H0: The mean value of accounts receivable = $260.00
Ha: The mean value of accounts receivable ≠ $260.00

2. To calculate the test statistic, you need to use the formula for the t-test:

t = (sample mean - hypothesized mean) / (sample standard deviation / √sample size)

Given:
Sample mean (x̄) = $250.00
Hypothesized mean (μ0) = $260.00
Sample standard deviation (σ) = $43.00
Sample size (n) = 36

Plugging the values into the formula:
t = ($250.00 - $260.00) / ($43.00 / √36)

Simplify:
t = (-$10.00) / ($43.00 / 6)

Calculate:
t ≈ -1.395

Therefore, the test statistic (t) is approximately -1.395.

3. To find the p-value, you need to consult a t-distribution table or use statistical software. The p-value is the probability of obtaining a test statistic at least as extreme as the observed value, assuming the null hypothesis is true.

Given that the level of significance is 5% (or α = 0.05), you want to compare the p-value to this threshold value.

For a two-tailed test (since the alternative hypothesis is two-sided), you need to find both the left-tail and right-tail probabilities.

Using the t-distribution table or software, calculate the probabilities for t < -1.395 and t > 1.395. These probabilities correspond to the areas under the t-distribution curve.

Let's assume the p-values are P(L) and P(R) for the left-tail and right-tail probabilities, respectively.

The p-value is calculated as P = P(L) + P(R).

Compare the p-value to the chosen significance level (α) of 0.05. If the p-value is less than α, you reject the null hypothesis.

Note: Without specific values for P(L) and P(R), I cannot provide the exact p-value for this question. You would need to consult a t-distribution table or statistical software to obtain the probabilities and calculate the p-value.