Question

In a study of parents' perceptions of their children's size, researchers asked parents to estimate their youngest child's height. The researchers hypothesize that parents tend to underestimate their youngest child's size because the youngest child is the baby of the family and all other family members appear larger compared to the baby. The sample of 39 parents who were surveyed underestimated their youngest child's height by 7.5 cm on average; the standard deviation for the difference in actual heights and estimated heights was 7.2 cm, and the data were approximately normal. Determine the TS and p-value for this study.

A) TS = 6.51, p-value = 0.0000
B) TS = -6.51, p-value = 0.0000
C) TS = -1.04, p-value = 0.1492
D) TS = 1.04, p-value = 0.1492

Answer 1

B) TS = -6.51, p-value = 0.0000

Explanation:

Sample size, n = 39

μ = 7.5 cm

Null hypothesis, H₀ = 7.5 cm

(I.e. Average height of youngest child is 7.5 cm)

Alternative hypothesis,
`H_(a)\\eq 7.5` (The youngest child's age is underestimated by 7.5 cm)

Standard deviation,
`\sigma = 7.2 cm`

In order to be able to reject the null hypothesis,

the formula for the test statistic:

`t = (- \mu)/(s/√(n) )`

`t = (- 7.5)/(7.2/√(39) )`

t = -6.51

P - value

P(x < 7.5) = P(z < -6.51)

Checking the p-value for z < -6.51 in the normal distribution table

P(z < -6.51) = 0.0000

p - value = 0.0000