Aim: To Calculate Sample Size required to test whether a sample mean is significantly different than a known / hypothesized mean.

Formula Used

For two tailed hypothesis

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For one tailed hypothesis

μ_T = Estimated sample mean.

μ_K = Hypothesised mean against which sample mean is compared.

SD_T = Estimated standard deviation in sample.

Z _1-α = the standard normal deviate corresponding the confidence level

β = 1 – Power (Out of 1) (e.g. 80% = 0.8)

Z _1-β = the standard normal deviate corresponding to 1- β.

Example 1:

A new antihypertensive drug is to be tested to find whether mean reduction in SBP with this test drug is significantly different than an hypothesised value of 25. The test drug is expected to reduce the SBP by 28 mm of Hg with SD of 6. How much sample size shall be required at confidence level of 95% and power of 80%.

Solution:

Here

μ_T = 28, μ_K = 25, SD_T = 6, confidence level = 95%, power = 80%, two tailed ("significantly different")

After putting these values, we get required sample size = 31.

Example 2:

A new antihypertensive drug is to be tested to find whether mean reduction in SBP with this test drug is significantly more than an hypothesised value of 25. The test drug is expected to reduce the SBP by 28 mm of Hg with SD of 6. How much sample size shall be required at confidence level of 95% and power of 80%.

Solution:

Here

μ_T = 28, μ_K = 25, SD_T = 6, confidence level = 95%, power = 80%, one tailed ("significantly more")

After putting these values, we get required sample size in each group = 25.