Question

Explain what is wrong with each set of null and alternative hypotheses shown. Then, correct each to form a proper set of hypotheses.

A) H0: p ̂=0.50, Ha:p ̂>0.50

B) H0: μ=100, Ha: μ=200

C) H0: p=0.30, Ha: p > 0.10

Answer 1

Solution:

we have to explain what is wrong with each set of null and alternative hypotheses shown and then we have to correct each to form a proper set of hypotheses.

Please note following conditions to answer:

i) we state hypothesis about population parameters, not the sample statistics. So hypothesis should include population parameters like population mean μ , population proportion p etc.

ii) Null hypothesis is hypothesis of no difference or it is always = type whereas alternative hypothesis is opposite to null hypothesis. It may be < type or > type or type depending on what we have to test.

iii) Values stated for parameters in null hypothesis should be same in alternative hypothesis.

Now consider A)

Part A) H0: p^ =0.50, Ha:p^ >0.50

Here hypothesis is stated about the sample proportion which is not correct. It should be population proportion p.

From above three conditions , condition ii) and iii) are satisfied except condition i)

Thus correct hypotheses are:

H0: p = 0.50       , Ha: p > 0.50

Part B) H0: μ=100, Ha: μ=200

Here condition i) is satisfied but condition ii) and iii) doesn't satisfied

alternative hypothesis should be one of the < type or > type or type.

Since we do not know whether is < type or > type,we will use type.

Also parameter value stated in Ha is different from H0.

Thus correct set of hypothesis are:

H0: μ=100, Ha: μ 100.

Part C) H0: p=0.30, Ha: p > 0.10

Here condition i) and ii) are satisfied but not the condition iii)

Parameter value stated in H0 is different from parameter value stated in Ha.

So it should be same.

Thus correct set of hypothesis are:

H0: p=0.30, Ha: p > 0.30