z-statistic

[sks2013]

Given the following hypothesis:
The null hypothesis is H0 : µ = 5
The alternative is H1 : µ ≠ 5
The mean of a sample of 17 is 7
The population standard deviation is 2.0
What is the calculated z-statistic?

 

[S2000magician]

z = (x-bar − μ) / σ = (7 − 5) / 2 = 1.

 

[sks2013]

S2000magician wrote:
z = (x-bar − μ) / σ = (7 − 5) / 2 = 1.

S2000magician
the explanation given is as follows-
The z-statistic is calculated by subtracting the hypothesized parameter from the parameter that has been estimated and dividing the difference by the standard error of the sample statistic. Here, the test statistic = (sample mean − hypothesized mean) / (population standard deviation / (sample size)^1/2 = (X − μ) / (σ / n^1/2) = (7 − 5) / (2 / 17^1/2) = (2) / (2 / 4.1231) = 4.12.

 

[S2000magician]

Aha!
They’re quite correct, and I apologize for my error. I answered far too hastily.
This is a test of the mean, so the correct denominator is the standard error, which is σ/√n.
Don’t I feel like an idiot.
Carry on.

 

[sks2013]

you are always right. so i was having doubt, whether the explanation is wrong or you have made one mistake.
rgds—-

 

[S2000magician]

Every once in a while I’m right.
Don’t give me too much credit.

 

[sks2013]

i am following you since some time to the posts you are making. so i know you are through in your matter.