How to determine the null and alternative hypotheses (under normal definition of p and μ)?

Question

An IT team wants to see whether the mean lifetime of a VoIP communication is more than 4 minutes so that they can go in to investigate any calls outside of that duration. The team has indicated that they think that the average lifetime is about 4 minutes.

Answer 1

The null hypothesis (H₀) is that the mean (μ) is 4 minutes. The alternative hypothesis (H₁ or H_a) in this case is that the mean>4 minutes. The purpose of hypothesis testing is to carry out a test which determines whether (within a specified confidence interval) the null hypothesis is to be rejected. When it is rejected it makes it more likely (but not certain) that the alternative hypothesis might be true.

The test usually establishes a critical p-value. If the test results are more extreme than this value (lower than), the null hypothesis has to be rejected within the frame of the specified confidence interval.

Comments

Based on above analysis; which of the below options we can say is more accurately fit to choose?

Select one:
A: H0: p=4 vs Ha: p>4
B: H0: μ=4 vs Ha: μ>4
C: H0: p=4 vs Ha: p≠4
D: H0: μ=4 vs Ha: μ<4

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Hello Rod, thank you for your help as always.

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Ha is μ>4, so option B.