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48. Did the randomization produce similar groups? First, compare the two groups of birds in the first year. The only difference should be the
chance effect of the random assignment. The study report says: 鈥淚n the experimental year, the degree of synchronization did not differ between
food-supplemented and control females.鈥 For this comparison, the report gives t=-1.05.
(a) What type of tstatistic (one-sample, paired, or two-sample) is this? Justify your answer.
(b) Explain how this value of t leads to the quoted conclusion.

Short Answer

Expert verified

(a) The two-sample is the tstatistic.

(b) Insufficient evidence to support the quoted conclusion.

Step by step solution

01

Part (a) Step 1: Given information

To find that the givent statistic is one-sample, paired, or two-sample.

02

Part (a) Step 2: Explanation

Two sets of birds are compare to the test.
The first group consists of 7pairings, while the second group consists of 6pairs.
Because the sample sizes differ, paired data cannot be included in the samples.
As a result, the two-sample is thet statistic

03

Part (b) Step 3: Explanation

To explain the value of t leads to the quoted conclusion.

04

Part (b) Step 4: Explanation

Let, the statistic t=-1.05

Find the null and alternative hypotheses:
Ho:1=2
Ha:12
Find the degree of freedom as:
df=minn1-1,n2-1

=min(7-1,6-1)

=5

Using table B, calculate the p-value as:

p-value=2P(t>1.05)

=0.342

Note that, p-value is greater than the significance level.

When the P-value is less than or equal to the significance level, then the null hypothesis will be rejected:
P>0.05Fail to rejectH0

The null hypothesis is not rejected.

Hence, there is insufficient evidence to support the quoted conclusion.

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