Answered

Camila is curious about the average length of the female blue whales her organization monitors. She takes a
random sample of 4 female blue whales from this population. Their average recorded length is ő = 78 m and
their standard deviation is 8. = 10 m. The distribution of lengths in the sample is roughly symmetric with no
obvious outliers.
Based on this sample, which of the following is a 95% confidence interval for the mean length (in meters) of
female blue whales?
Choose 1 answer
(46.18, 109.82)
B
(62.09, 93.91)
(66.24, 89.77)

Answer :

Using the t-distribution, as we have the standard deviation for the sample, the 95% confidence interval is (71.63, 84.36).

What is a t-distribution confidence interval?

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

  • [tex]\overline{x}[/tex] is the sample mean.
  • t is the critical value.
  • n is the sample size.
  • s is the standard deviation for the sample.

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 4 - 1 = 3 df, is t = 3.1824.

The parameters are given as follows:

[tex]\overline{x} = 78, s = 10, n = 4[/tex]

Hence, the bounds of the interval are given by:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 78 - 3.1824\frac{10}{\sqrt{4}} = 71.63[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 78 + 3.1824\frac{10}{\sqrt{4}} = 84.36[/tex]

The 95% confidence interval is (71.63, 84.36).

More can be learned about the t-distribution at https://brainly.com/question/16162795

my1stcatsnameisfrost

Answer:

(62.09, 93.91)

Step-by-step explanation:

The correct answer on Khan

${teks-lihat-gambar} my1stcatsnameisfrost

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