Nearpod Question 1

4 pts

Use this scenario to complete the parts that follow.

Scenario: Maximus went on a run. After 12 seconds he ran 72 yards.

Independent & Dependent:

In this situation seconds

is the independent variable (x) and

yards

is the dependent variable (y).

Unit Rates

Maximus can run

yards in 1 second.

In (Select)

seconds, Maximus can run 1 yard,

(a): The 95% confidence interval is (46.4, 53.6)

(b): The 95% confidence interval is (47.9, 52.1)

(c): Larger sample gives a smaller margin of error.

Step-by-step explanation:

Given

-- sample size

-- sample mean

--- sample standard deviation

Solving (a): The confidence interval of the population mean

Calculate the standard error

The 95% confidence interval for the z value is:

Calculate margin of error (E)

The confidence bound is:

--- approximated

--- approximated

So, the 95% confidence interval is (46.4, 53.6)

Solving (b): The confidence interval of the population mean if mean = 90

First, calculate the standard error of the mean

The 95% confidence interval for the z value is:

Calculate margin of error (E)

The confidence bound is:

--- approximated

--- approximated

So, the 95% confidence interval is (47.9, 52.1)

Solving (c): Effect of larger sample size on margin of error

In (a), we have:

In (b), we have:

Notice that the margin of error decreases when the sample size increases.