Null hypothesis?

Question

3. μ = 75, σ = 7.5, N = 10 α = .05 What values of (X bar) would lead to rejection of the null hypotheses if:
(a) the test was non directional
(b) if Ho stated that (X bar) ≤ μ and
(c) if Ho stated (X bar)  ≥ μ?

Answer 1

(a) You would reject the null if xbar is too large or too small. Since alpha is 0.05, then you would reject if |z| > 1.96, mean that either z > 1.96 or z < -1.96. Now

z = (xbar-mu)/(sigma/sqrt(n))
= (xbar-75)/sqrt(7.5/sqrt(10))

So set z to be either 1.96 or -1.96 to get your answer.

1.96 = (xbar-75)/sqrt(7.5/sqrt(10)) and solve for xbar.

Thus you would reject the null if xbar is larger than 79.649.

-1.96 = (xbar-75)/sqrt(7.5/sqrt(10))

You would also reject the null if xbar is smaller than 70.351.

(b). This time you would reject if xbar is too large. In terms of z, you would reject if z > 1.645 since alpha is 0.05. So use the same method as before.

1.645 = (xbar-75)/sqrt(7.5/sqrt(10)) and solve for xbar.

You would get 79.139. You would reject the null if xbar is larger than 79.139.

(c) Same as above, except this time you reject if xbar is too small. Use z = -1.645.

-1.645 = (xbar-75)/sqrt(7.5/sqrt(10)) and solve for xbar.

You would reject the null if xbar is less than 70.861.

Answer 2

Null speculation is a term in statistic. in case you want i will describe it to you with out jargon. In experimental psychology we use it to answer the assertion of the situation and to teach the different effect of what's envisioned. it may additionally advise that the self sufficient variable did not effect to any distinction or effect to the based variable. to illustrate: My thesis exchange into relating to the effect of Dance circulation treatment to the vanity of sexually abused little ones. the alternative speculation to be examined is: H1 (Stands for selection or what you assume the learn how to effect to): there is an substantial distinction on the point of vanity of the contributors after the intervention is equipped. And the null speculation in this learn exchange into: H0: there is not any substantial distinction on the point of self–esteem of the contributors after the intervention. wish to have helped you!

Answer 3

I think your null hypothesis in all cases is that m = 75

So in a) your alternative is m =/= 75, so it's a two tailed test

b) < means it's left tailed

c) > mean its right tailed.