Assume that the amount of beverage in a randomly selected 16-ounce beverage can has a normal distribution. Compute a 99% confidence interval for the population mean amount of beverage in 16-ounce beverage cans and fill in the blanks appropriately.

A 99% confidence interval for the population mean amount of beverage in 16-ounce beverage cans is ( , ) ounces. (round to 3 decimal places)

Answer:

$99\% \: \text {confidence interval} = (14.886, \: 16.113)\\\\$

Therefore, the 99% confidence interval for the population mean amount of beverage in 16-ounce beverage cans is (14.886, 16.113) ounces.

Step-by-step explanation:

Let us find out the mean amount of the 16-ounce beverage cans from the given data.

Using Excel,

=AVERAGE(number1, number2,....)

The mean is found to be

$\bar{x} = 15.5$

Let us find out the standard deviation of the 16-ounce beverage cans from the given data.

Using Excel,

=STDEV(number1, number2,....)

The standard deviation is found to be

$s = 0.4957$

The confidence interval is given by

$\text {confidence interval} = \bar{x} \pm MoE\\\\$

Where $\bar{x}$ is the sample mean and Margin of error is given by

$$ MoE = t_{\alpha/2} \cdot (\frac{s}{\sqrt{n} } ) $ \\\\$

Where n is the sample size, s is the sample standard deviation and is the t-score corresponding to a 99% confidence level.

The t-score corresponding to a 99% confidence level is

Significance level = α = 1 - 0.99 = 0.01/2 = 0.005

Degree of freedom = n - 1 = 8 - 1 = 7

From the t-table at α = 0.005 and DoF = 7

t-score = 3.4994

$MoE = t_{\alpha/2}\cdot (\frac{s}{\sqrt{n} } ) \\\\MoE = 3.4994 \cdot \frac{0.4957}{\sqrt{8} } \\\\MoE = 3.4994\cdot 0.1753\\\\MoE = 0.6134\\\\$

So the required 99% confidence interval is

$\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 15.5 \pm 0.6134\\\\\text {confidence interval} = 15.5 - 0.6134, \: 15.5 + 0.6134\\\\\text {confidence interval} = (14.886, \: 16.113)\\\\$

Therefore, the 99% confidence interval for the population mean amount of beverage in 16-ounce beverage cans is (14.886, 16.113) ounces.

8 0

4 years ago

Isabel’s team won their baseball game and scored 60 points total . If Isabel scored 12 of the points and everyone else scored 8

Studentka2010 [4]

Answer:

6 people on her team

Step-by-step explanation:

60-12= 48

48/8= 6

6 0

4 years ago

Read 2 more answers

3HELP__________________

Brut [27]

Answer:

m∠KIJ = m∠LIM ⇒ answer B

Step-by-step explanation:

* Lets explain how to solve the problem

∵ I is the mid-point of NH

∴ IN = IH

- MJ is perpendicular to NH and passes through I the mid-point of NH

∴ MJ is perpendicular bisector of NH

- NH ⊥ MJ and intersects it at I

∴ m∠NIM = m∠NIJ = 90°

- ∠ NIM consists of two angles ∠NIL and ∠MIL

∵ m∠NIM = m∠NIL + m∠MIL

- ∠NIJ consists of two angles ∠NIK and ∠JIK

∵ m∠NIJ = m∠NIK + m∠JIK

∴ m∠NIL + m∠MIL = m∠NIK + m∠JIK ⇒ (1)

∵ NH bisects ∠KIL

∴ m∠NIL = m∠NIK ⇒ (2)

- From (1) and (2)

∴ m∠MIL = m∠JIK

* m∠KIJ = m∠LIM

7 0

3 years ago