Question

In each of the following situations, is the alternative hypothesis one-tailed or two-tailed? What are the hypotheses?

a) A soda company recently reformulated their diet cola in an attempt to appeal to teenagers. They run a taste test to see if the new formula appeals to more teenagers than the standard formula.

b) A budget override in a small town requires a two-thirds majority to pass. A local newspaper conducts a poll to see if there's evidence it will pass.

c) One financial theory states that the stock market will go up or down with equal probability. A student collects data over several years to test the theory.

a) Is the part a alternative hypothesis one-tailed or two-tailed?
A. Two-tailed

B. One-tailed

State the null and alternate hypotheses for the approval of the new formula. Fill in the correct symbols below.

H₀: Approval New ___ (pick: <, >, =, ≠) Approval Old

H_A: Approval New ___ (pick: <, >, =, ≠) Approval Old

b) Is the part b alternate hypothesis one-tailed or two-tailed?

A. One-tailed

B. Two-tailed

State the null and alternate hypotheses for the poll on the budget override. Fill in the correct symbols below.

H₀: Voters for the budget ___ (pick: <, >, =, ≠) 2/3

H_A: Voters for the budget  ___ (pick: <, >, =, ≠) 2/3

c) Is the part c alternate hypothesis one-tailed or two-tailed?

A. One-tailed

B. Two-tailed

State the null and alternate hypotheses for the theory of fluctuations in the stock market. Fill in the correct symbols below.

H₀: P_{stocksgo up} ___ (pick: <, >, =, ≠) P_{stocks go down}

H_A: P_{stocksgo up} ___ (pick: <, >, =, ≠) P_{stocks go down}

Answer 1

a) The soda company wants to test if the new formula appeals more than the old formula.so this is a one tailed test. So option B is correct.

Our hypothesis is:

H0: Approval New = Approval Old

vs HA: Approval New> Approval Old

b) To check the evidence that budget override passes we need more than 2/3rd to pass. So this is a One tailed test.

So option B is correct.

Our hypothesis is:

H0: Voters for the budget= 2/3

vs HA: Voters for the budget >2/3

c) To test if the stock market goes up or down with equal probability, we have a two tailed test. So option A is correct.

Our hypothesis is:

H0: p stocks go up = p stocks go down

vs HA: p stocks go up is not equal to p stocks go down.