7.3.5 In a study of parents’ perceptions of their children’s size, researchers K

Question

7.3.5
In a study of parents’ perceptions of their children’s size, researchers Kaufman et al. (Current Biology, 2013) asked parents to estimate their youngest child’s height. The researchers hypothesized that parents tend to underestimate their youngest child’s size because the youngest child is the baby of the family and everybody else is the family appears bigger compared to the baby.
The researchers also surveyed a sample of 36 parents about their eldest child’s height. The parents overestimated their eldest child’s height by 0.52 cm, on average; the standard deviation for the difference in actual heights and estimated heights was 5.2 cm without strong skewness in the data.

1)Is there evidence that parents tend to either over- or under-estimate eldest children’s heights? Carry out a theory-based test using an appropriate applet or statistical software. Find and report a p-value as well as a standardized statistic. Round the test statistic to 2 decimal places, e.g. 5.83, and the p-value to 4 decimal places, e.g. 0.0583.

t= ?? p value = ??

2) Using an appropriate applet or statistical software, find a 95% confidence interval for the difference. Round your answers to 2 decimal places, e.g. 5.83.

3) We have found a very significant difference in the actual and estimated average heights of eldest children by their parents, with parents, on average, estimating the height of their oldest child between $ll1 and $ul cm more than actual height.

true

false

4) What assumption do you have to make about the data in order for the validity conditions of the appropriate theory-based test to be satisfied?

There is not strong skewness in the distribution of differences in actual and estimated heights.

There is strong skewness in the distribution of differences in actual and estimated heights.

The sample size is larger.

The sample size is smaller.

There is not strong skewness in the distribution of differences in actual and estimated heights.

Explanation / Answer

Sample size = 36

Null Hypothesis : H0 : The parents don't underestimate or overestimated their eldest child’s height. d =0

Alternative Hypothesis : Ha : The parents overestimateor underestimate their eldest child's height. d 0

Test Statistic

t = d /(sd /sqrt(n) ) = 0.52/ (5.2/sqrt(36)) = 0.52/ (5.2/6) = 0.6

p -value (dF = 35) = 2* Pr ( t >=0.6) = 0.5524

(2) 95% confidence interval = xd +- t0.95,35 sd /sqrt(n)

= 0.52 +- 2.03 * 5.2/sqrt(36)

= 0.52 +- 2.03 * 0.867

= (-1.24 cm, 2.28 cm)

3) We have found a very significant difference in the actual and estimated average heights of eldest children by their parents, with parents, on average, estimating the height of their oldest child between $ll1 and $ul cm more than actual height.

Answer : Here, we will not be able to reject null hypothesis so The answer is False.

4) assumptions : There is not strong skewness in the distribution of differences in actual and estimated heights.

Option A is correct.

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