To determine if the company's support performance is statistically different from the industry standard, we can conduct a hypothesis test. Since we're comparing a sample mean to a known population mean, a one-sample $t$-test is appropriate, assuming the population standard deviation is unknown.

Steps for Hypothesis Testing:

1. Null Hypothesis (H₀):

   • The company's mean resolution time is equal to the industry standard.
   • $H_0: \mu = 20$ minutes.

2. Alternative Hypothesis (H₁):

   • The company's mean resolution time is different from the industry standard.
   • $H_1: \mu \neq 20$ minutes.

3. Given Data:

   • Population mean (industry standard), $\mu = 20$ minutes.
   • Sample mean, $\bar{x} = 21$ minutes.
   • Sample standard deviation, $s = 7$ minutes.
   • Sample size, $n$ (Not given explicitly, so assume or denote as $n$).

4. Test Statistic: The formula for the $t$-test statistic is:

   $t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$

   Plugging in the values:

   $t = \frac{21 - 20}{\frac{7}{\sqrt{n}}} = \frac{1}{\frac{7}{\sqrt{n}}}$

5. Determine Degrees of Freedom: Degrees of freedom $df = n - 1$.

6. Find the Critical Value or P-value: Based on the calculated $t$-value and degrees of freedom, compare this with the critical $t$-value from the $t$-distribution table (or use the P-value).

7. Decision:

   • If the calculated $t$-value is greater than the critical $t$-value (or the P-value is less than the significance level, typically 0.05), reject the null hypothesis.
   • Otherwise, do not reject the null hypothesis.

To proceed with the calculation, I need the sample size $n$. Could you provide that information, or would you like to assume a typical value for $n$?

---

Follow-up Questions:

1. What is the sample size $n$ for the company data?
2. Would you like to assume a significance level for the test (e.g., 0.05)?
3. Do you have any additional performance metrics to analyze?
4. Would you prefer using a specific statistical software for the calculation?
5. Is there a need to adjust the performance based on other variables, like ticket complexity?

Tip:

Always ensure that the sample size is sufficient for hypothesis testing to improve the accuracy and reliability of the results.