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hjlf
3 years ago
14

The sodium content of a popular sports drink is listed as 200 mg in a 32-oz bottle. Analysis of 20 bottles indicates a sample me

an of 211.5 mg with a sample standard deviation of 18.5 mg.
(a)
State the hypotheses for a two-tailed test of the claimed sodium content.
H0: µ = 200 vs. H1: µ ≠ 200
H0: µ ≥ 200 vs. H1: µ < 200
H0: µ ≤ 200 vs. H1: µ > 200

(b)
Calculate the t test statistic to test the manufacturer’s claim.


(c)
At the 5 percent level of significance (α = 0.05) does the sample contradict the manufacturer’s claim?
__(reject or do not reject)____ H0. The sample _____(contradict or does not contradict)______ the manufacturer's claim.


(d-1)
Use Excel to find the p-value and compare it to the level of significance.
Did you come to the same conclusion as you did in part (c)?
Mathematics
1 answer:
julia-pushkina [17]3 years ago
4 0

Answer:

The sample does not contradicts the manufacturer's claim.

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 200 mg

Sample mean, \bar{x} = 211.5 mg

Sample size, n = 20

Alpha, α = 0.05

Sample standard deviation, s = 18.5 mg

a) First, we design the null and the alternate hypothesis  for a two tailed test

H_{0}: \mu = 200\\H_A: \mu \neq 200

We use Two-tailed t test to perform this hypothesis.

b) Formula:

t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} } Putting all the values, we have

t_{stat} = \displaystyle\frac{211.5 - 200}{\frac{18.5}{\sqrt{20}} } = 2.7799

c) Now,

t_{critical} \text{ at 0.05 level of significance, 19 degree of freedom } = \pm 2.0930

Since, the calculated t-statistic does not lie in the range of the acceptance region(-2.0930,2.0930), we reject the null hypothesis.

Thus, the sample does not contradicts the manufacturer's claim.

d) P-value = 0.011934

Since the p-value is less than the significance level, we reject the null hypothesis and accept the alternate hypothesis.

Yes, both approach the critical value and the p-value approach gave the same results.

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If D is the center of the circle below and AC measures 48, what is the measure of ABC
dimulka [17.4K]

Answer:

24

Step-by-step explanation:

How do we know that a circle must complete up to 180, then we have to:

180 - 48 = 132

Now knowing this distance we can also know the other, starting from the same concept, in addition to what the circle below is like, a semicircle refers to so we divide by 2:

(180-132) / 2 = 24

Therefore the answer is 24.

We can also do it ABC is half of ADC. So ABC = 48/2 = 24

4 0
2 years ago
The line for the equation y = 1 horizontal or vertical? What is the slope of this line?
Nimfa-mama [501]

Answer:

The line is horizontal and the slope is 0.

Step-by-step explanation:

Any line that is horizontal has a slope of 0.

7 0
2 years ago
Use the graph to determine the vertex point of the quadratic function. Is the vertex a
Feliz [49]

Answer:

B) Vertex (1,2), maximum

Step-by-step explanation:

First, determine if the graph has a maximum or a minimum value. Since the graph opens downwards, it has a <u>maximum</u> value.

The maximum is the point that has the greatest y value. We can see that the greatest y value is at y=2. Going down two units from that spot, we can see that the x value is at x=1. We can plug those into the vertex form, (x,y). By plugging in we get the point (1,2).

5 0
2 years ago
How would you solve that problem
antiseptic1488 [7]
Since you that that line is 180 degrees you can simply do 180-149 and find that the answer is 31 degrees. So you would do 13x+5=31, 31-5=26, 26/13, and then x=2 :)
7 0
3 years ago
Tisha and her academic team are working to go to state finals. They must have a certain number of points to advance. They have h
Westkost [7]

Answer:

b equals T minus a minus c minus d all over 3 ⇒ 3rd answer

Step-by-step explanation:

* Lets explain how to solve the problem

- Tisha and her academic team have had three local matches

# Assume that the points of the local matches are a , c , d

- They will attend a district match

- District match points count for three times the number of points

  than local matches do

# Assume that the points of the district match is b

- T is the total points they will earned in the four matches

∵ The points in the local matches are a , c , d

∵ The point in district mach is 3b

∴ T = a + c + d + 3b

* <u><em>Lets find b in terms of a , c , d , T</em></u>

∵ T = a + c + d + 3b

- Subtract a from both sides

∴ T - a = c + d + 3b

- Subtract c from both sides

∴ T - a - c = d + 3b

- Subtract d from both sides

∴ T - a - c - d = 3b

- Divide both sides by 3

∴ b=\frac{T-a-c-d}{3}

∴ b equals T minus a minus c minus d all over 3

4 0
3 years ago
Read 2 more answers
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