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 35 parents about their eldest child's height. The parents overestimated their eldest child's height by 0.49 cm, on average; the standard deviation for the difference in actual heights and estimated heights was 4.9 cm without strong skewness in the data. 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. , p-value (two-sided test) 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. Confidence interval(

Answer 1

Sample size, n = 35

Eldest child's average height, $\bar x_d$ = 0.49

Standard deviation for the difference, $s_d$ = 4.9

Null and Alternative hypothesis:

$H_o:\mu_d =0$

$H_a:\mu_d \neq0$

1) Test statistic:

$t = \frac{\bar x_d}{s_d/\sqrt{n}} = \frac{ 0.49}{ 4.9/\sqrt{ 35}} =\textbf{ 0.59}$

df = 35-1 = 34

P-value = 0.5591

2) At $\alpha$ = 0.05 and df = 34, critical value _{$t_{\alpha/2}$} = 2.032

Confidence interval:

$\left (x_d \pm t_{\alpha/2}*\frac{s_d}{\sqrt{n}} \right )$

$\left (0.49 \pm 2.032*\frac{4.9}{\sqrt{35}} \right )$

$\left (\textbf{ -1.19, 2.17} \right )$

3) Conclusion:

As p-value = 0.5591 > 0.05, we fail to reject the null hypothesis.

Answer : False

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