Question

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 (SSD)

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.

**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:-**

**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 = 6 -1

**D.F = 5**

**Step3)**

**t _{critical} = - 1.476**

Step 4)

**S.S = 5.5**

s = sqrt [ (\sum (d_{i} - d)^{2} / (n - 1) ]

**s = 1.0488**

SE = s / sqrt(n)

**S.E = 0.42817**

**Step 5)**

t = [ (x_{1} - x_{2}) - D ] / SE

**t = - - 3.50**

**Step 6)**

**Since t _{obtained} (-3.50) is less than the
t_{critical}(-1.426) 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 5 degrees of freedom is less than - 3.50

**Thus, the P-value = 0.009.**

**Interpret results. Since the P-value (0.009) is less
than the significance level (0.10), 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 kids take more candy under
conditions that make them feel anonymous.**

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