Question

The mean of the sample is 9.771 km/h , and the standard deviation is 0.944 km/h . Construct and interpret a 95 percent confidence interval for the mean swimming speed of all emperor penguins in the population.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The confidence interval for the mean swimming speed of all emperor penguins in the sampled population is (9.4248, 10.1172).

Given the following data:

• Mean of a sample = 9.771 km/h

• Standard deviation = 0.944 km/h

• Confidence interval = 95% = 0.95

• Sample size = 31

What is a confidence interval?

In Statistics, a confidence interval can be defined as the degree of uncertainty that is associated with a given statistical population.

How to calculate confidence interval

First of all, we would subtract one from the given sample size for penguins.

$n=31-1=30$

Next, we would subtract the confidence interval from 1 and then divide by 2:

$\frac{(1-0.95)}{2} =\frac{0.05}{2} =0.025$

From the t-distribution table, a 30 degree of freedom (df) with 0.025 is equal to 2.042.

Divide the standard deviation by the square root of penguin's population size and then multiply by the t-interval.

$\frac{0.944}{\sqrt{30} } \times 2.042=0.3462$

For the lower end:

$9.771-0.3462=9.4248$

For the upper end:

$9.771+0.3462=10.1172$

Therefore, the confidence interval for the mean swimming speed of all emperor penguins in the sampled population is (9.4248, 10.1172).

Read more on confidence interval here: https://brainly.com/question/15712887