Get the solution to "The following data reprents the age (in weeks)..."

krypsojx

Answered question

2021-11-29

The following data reprents the age (in weeks) at which babies first crawl based on a survey of 14 mothers.
52,30,44,35,39,26,47,37,56,26,39,28,38,34
Construct and interpret a 90% confidence interval for the mean age at which a baby first crawls.

Answer & Explanation

Fesion

Beginner2021-11-30Added 24 answers

Step 1
given data,

n = 14 ∴ d f = n - 1 = 14 - 1 = 13

Sample mean

\overset{―}{x} = \frac{\sum x_{i}}{n}

= \frac{52 + \dots + 34}{14}

= 37.9286

s^{2} = \frac{\sum_{1 = 1}^{n} {(x_{i} - \overset{―}{x})}^{2}}{n - 1}

= \frac{S S}{n - 1}

= \frac{1116.9286}{14 - 1}

= 85.91758

s = 9.2692

Step 2
for 90% ,

α = 1 - 0.90 = 0.10

t_{c} = t_{\frac{α}{2}, d f} = t_{\frac{0.10}{2}, 13}

c 1, (\overset{―}{x} \pm E) = (\overset{―}{x} \pm t_{c} \cdot \frac{s}{\sqrt{n}})

= (37.9286 \pm 1.770 \cdot \frac{9.2692}{\sqrt{14}})

= (37.9286 \pm 4.3848) = (33.54, 42.31)

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