Question

In answering the question(s), make sure to write down the following 7 steps.

Step 1: Establish null and alternate hypotheses- State the null and alternative hypothesis (as a sentence and formula).

Step 2: Calculate the degrees of freedom

Step 3: Calculate t _critical using critical t – table

Step 4: Calculate the Sum of Square deviation (SS_D)

Step 5: Calculate t _obtained

Step 6: Specify the critical value and the obtained value on a t-distribution curve

Step 7: Decision and Conclusion- Write a clear and concise conclusion.

1. A Pullman local sports store is interested in consumer purchasing likelihood of WSU gear (1=not at all to 7=very much) before and after a win in football. A researcher picks 10 WSU students as the participants of the study. The data are shown below. Use alpha = .01 to see whether a win in football increases consumers’ likelihood of buying WSU gear.

After: 4 5 5 6 5 7 5 6 3 4

Before: 3 5 4 4 5 6 5 4 3 3

2. A marketing researcher has heard that when kids are anonymous, they'll take more candy. To test this hypothesis, she brings 6 kids into a specially-constructed Halloween Lab with two rooms. Each room is identically decorated and contains a decorated front porch, a front door, and a doorbell. Behind the door is a confederate who will answer the door and offer a bowl of candy. The two rooms differ only in their lighting conditions. One room is light; one room is dark, the latter presumably leading to greater anonymity. She says, ok kids, I want you to go into each room and interact with the person behind the door as you would normally interact during Halloween. Ring the doorbell, say trick or treat, and then take some candy. So, the kids do this and the researcher measures how many pieces of candy they take. The data are shown below. Do kids take more candy under conditions that make them feel anonymous? Use alpha = .10.

Light Room:                              1                2                1                1                2                2

Dark Room:                              2                2                3                4                4                3

Answer 1

Solution:-

1)

Step1)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u_d> 0

Alternative hypothesis: u_d < 0

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.01. Using sample data, we will conduct a matched-pairs t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard deviation of the differences (s), the standard error (SE) of the mean difference, the degrees of freedom (DF), and the t statistic test statistic (t).

Step2)

DF = n - 1 = 10 -1

D.F = 9

Step3)

t_critical = -2.822

Step 4)

S.S = 5.6

s = sqrt [ (\sum (d_i - d)² / (n - 1) ]

s = 0.78881

SE = s / sqrt(n)

S.E = 0.24944

Step 5)

t = [ (x₁ - x₂) - D ] / SE

t = - 3.21

Step 6)

Since t_obtained (-3.21) is less than the t_critical(-2.822) hence we have to reject the null hypothesis.

where d_i is the observed difference for pair i, d is mean difference between sample pairs, D is the hypothesized mean difference between population pairs, and n is the number of pairs.

Since we have a one-tailed test, the P-value is the probability that a t statistic having 9 degrees of freedom is less than - 3.21.

Thus, the P-value = 0.005

Interpret results. Since the P-value (0.005) is less than the significance level (0.01), we have to reject the null hypothesis.

Step7)

Reject H0. From the above test we have sufficient evidence in the favor of the claim that win in football increases consumers’ likelihood of buying WSU gear.