The birth weights (in kilograms) of 5 elephants, selected randomly, are 133, 120, 97, 106, 124 (Source: www.elephant.se). Below are the summary statistics of the data and output from the analysis testing if the true average birth weight of the elephants is 100 kg.

min Q1 median Q3 max mean sd n missing

97 106 120 124 133 116 14.40 486 5 0

t = 2.4837, df = 4, p-value = 0.06794

alternative hypothesis: true mean is not equal to 100 95 percent confidence interval:

XXXXXX XXXXXX

What is the correct calculation of a 95% confidence interval for the true average birth weight of elephant?

(i) 116± 1.96 x 14.4

(ii) 116 ± 1.96 x 14.4/15

(iii)116 ±1.96 x 14.4/14

(iv) 116 ± 2.4837 x 14.4

(v) 116 ±2.4837 x 14.4/15

(vi) 116 ± 2.4837 14.4/74

(vii) 116 ± 2.78 x 14.4

(viii) 116 ± 2.78 x 14.4√5

(ix) 116 ±2.78 x 14.4√4

mean (sample mean) = 116 kg
standard deviation (sd) = 14.4 kg
sample size (n) = 5
t-value for 95% confidence interval with 4 degrees of freedom (df = n - 1) = 2.778

Now, we calculate the margin of error (ME):

ME = 2.778 * (14.4 / √5)

ME = 2.778 * (14.4 / 2.236)

ME ≈ 17.90

Then the 95% confidence interval (CI) is calculated as:

CI = 116 ± 17.90

So, the confidence interval is approximately (98.1, 133.9).

The correct choice among the provided options matches selection (viii) 116 ± 2.78 x 14.4/√5.

akiran007 akiran007 · Answer 2 · 2025-05-10T14:16:00-04:00

Answer:

(viii) 116 ± 2.78 x 14.4√5

Step-by-step explanation:

The given data is

Sample size =n= 5

Calculated t- value= 2.4837

Mean= 116

Standard deviation= sd= 14.40486

The t - value from table with 4 d.f for ∝/2 is t∝/2 (n-1)= 2.776

The 95% confidence interval is calculated by

d` ± t∝/2 (n-1) *sd/√n

Putting the values

116 ± 2.776* 14.40486/√5

Comparing these values with the options Part viii gives the best answer.

(viii) 116 ± 2.78 x 14.4√5

2.776 when rounded gives 2.78 and 14.40486 when rounded gives 14.4

The rest are incorrect.