Question

Suppose the null hypothesis is μ = 5 and we fail to reject it. Under this scenario, what can we conclude about the true population mean?

1) The true population mean is 5
2) The true population mean is not 5
3) The true population mean cannot be determined
4) The true population mean is less than 5

Answer 1

If we fail to reject the null hypothesis, we cannot conclude that the true population mean is different from the assumed value of 5.

Step-by-step explanation:

If we fail to reject the null hypothesis, which states that the population mean is μ = 5, it means that we do not have enough evidence to conclude that the true population mean is not 5. Therefore, we cannot conclude that the true population mean is different from 5. Option 2) The true population mean is not 5 is incorrect. Option 3) The true population mean cannot be determined is also incorrect. Option 4) The true population mean is less than 5 is also incorrect. The correct answer is option 1) The true population mean is 5.