clockwise swimming? 17. Male koalas bellows during the breeding season, but do f
ID: 3338800 • Letter: C
Question
clockwise swimming? 17. Male koalas bellows during the breeding season, but do females pay attention? Charlton et al. (2012) measured responses of estrous female koalas to playbacks of bellows that had been modified on the computer to simulate male call- ers of different body size. Females were placed one at a time into an enclosure while loudspeak- ers played bellows simulating a larger male on one side (randomly chosen) and a smaller male on the other side. Male bellows were played repeatedly, alternating between sides, over 10 minutes. Females often turned to look in the direction of a loudspeaker (invisible to her) during a trial. The following data measure the preference of each of 15 females for the sim- ulated sound of the "larger" male. Preference was calculated as the number of looks toward the larger-male side minus the number of looks to the smaller-male side. Preference is positive if a female looked most often toward the larger male, and it is negative if she looked most often in the direction of the smaller male. -2, 2, 6, 9, 13, 2, 5, 7, 2,-6, 4,3, 2,6,-6Explanation / Answer
Solution
Part (a)
Let X = difference in the number of looks.
Frequency Distribution of X
x
- 6
-2
2
3
4
5
6
7
9
13
Total
f
||
|
||||
|
|
|
||
|
|
|
15
The above frequency distribution does not exhibit any specific trend.
Part (b)
Testing
We assume that X ~ N(µ, 2) where µ = average difference in the number of looks over a 10-minute period and = standard deviation.
Claim:
Females do not pay attention to body cues in simulated male sounds. [i.e., average difference is zero.]
Hypotheses:
Null H0: µ = µ0 = 0 Vs Alternative HA: µ µ0
Test statistic:
t = (n)(Xbar - µ0)/s, where n = sample size; Xbar = sample average; s = sample standard deviation.
Summary of Excel Calculations is given below:
i
xi
1
-6
2
-6
3
-2
4
3
5
4
6
5
7
6
8
6
9
7
10
9
11
13
12
2
13
2
14
2
15
2
n
15
Xbar
3.133333
s
5.111146
s^2
26.12381
µ0 =
0
Xbar =
3.133333
s =
5.111146
tcal =
2.374291
Given =
0.05
tcrit =
2.144787
p-value
0.032425
Distribution, Critical Value and p-value
Under H0, t ~ tn – 1 [i.e., t-distribution with (n -1) degrees of freedom)
Critical value = upper (/2)% point of tn – 1.
p-value = P(tn – 1 > |tcal|)
Using Excel Function, tcrit and p-value are found to be: 2.145 and 0.03
Decision Criterion (Rejection Region)
Reject H0, if | tcal | > tcrit or p-value < .
Decision:
Since | tcal | > tcrit, H0 is rejected. Also confirmed by the p-value < .
Conclusion:
There is not sufficient evidence to support the claim. i.e., there is sufficient evidence to support that the females pay attention to body cues in simulated male sounds.
DONE
x
- 6
-2
2
3
4
5
6
7
9
13
Total
f
||
|
||||
|
|
|
||
|
|
|
15
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.