Question

How would you find the one sample z hypothesis testing using 4 steps for this question?

Answer 1

As no data is provided in the question, so, I will take a data to answer this question...

Question: Boys of a certain age in a certain locality have an average weight of 85 pounds. Somebody raised a complaint that the boys living in the slum area are underfed. For evidence, a sample of 25 boys of the same age were taken and then weighed and later it was determined that their average weight comes out to be 80.94 pounds. The population standard deviation for the locality is 11.6 pounds. On the basis of this, we need to make a conclusion...

Solution:

Hypothesis:

H₀: U > 85 (Null hypothesis)

H_a: U < 85 (Alternate Hypothesis)

It is a Single Tailed test (Lower Tail)

Here,

x¯ = 80.94

μ = 85

and σ = 11.6  

So,

Or, Z = (80.94 - 85)/{11.6/(25^1/2)}

Or, Z = - 1.75

At 95% confidence, Z is 1.65 and for the lower tail it is -1.65.

In this case, Z < −1.645.

So, we will not accept the null hypothesis as Z = −1.75 < −1.645, and it falls in the rejection zone.

End of the Solution...