Consider an upper-tail test of hypothesis for the difference in two population means. The sample data from the first population is: n = 50, x-bar = 110, s = 10. The sample data from the second population is: n = 75, x-bar = unknown, s = 11. We conclude the alternative hypothesis with a 2% level of significance. Then the value of the second sample mean must be?

To determine the value of the second sample mean, we need to perform an upper-tail test of hypothesis for the difference in two population means. Here are the steps to solve this problem:

Step 1: State the null and alternative hypotheses:
- Null hypothesis (H₀): The population means are equal.
- Alternative hypothesis (H₁): The population mean of the second population is greater than the population mean of the first population.

Step 2: Set the level of significance (α)
In this case, the level of significance is given as 2%. This means that we have a 2% chance of making a Type I error if we reject the null hypothesis.

Step 3: Calculate the critical value
Since this is an upper-tail test, we need to find the critical value from the t-distribution table. The critical value corresponds to the desired level of significance and the degrees of freedom, which is calculated as follows:
- Degrees of freedom (df) = (n₁ - 1) + (n₂ - 1)
- n₁ = sample size of the first population = 50
- n₂ = sample size of the second population = 75

Step 4: Perform the test statistic calculation
Calculate the test statistic using the formula:
- t = (x̄₁ - x̄₂) / √((s₁²/n₁) + (s₂²/n₂))
- x̄₁ = sample mean of the first population = 110
- x̄₂ = sample mean of the second population (unknown)
- s₁ = standard deviation of the first population = 10
- s₂ = standard deviation of the second population = 11

Step 5: Compare the test statistic with the critical value
If the test statistic is greater than the critical value, we reject the null hypothesis in favor of the alternative hypothesis.

To find the value of the second sample mean, we need the critical value for a 2% level of significance and the degrees of freedom. Please provide the degrees of freedom, or if not given, I can calculate them for you.