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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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3 years ago
A rhino can run 28 miles per hour. What is that speed in feet per second, to the nearest whole number?
Mrrafil [7]

Answer:

A rhino runs at a speed of about 28 miles per hour.

We need to determine the speed in feet per second.

Converting miles to feet:

The miles can be converted to feet by multiplying 5280 with 28 miles per hour.

Thus, we have;

28 x 5280 = 14784028 × 5280 = 147840

Thus, the speed of the rhino in feet per hour is 147840

Converting hours to seconds:

The hours can be converted into seconds by dividing 147840 by 3600 (Because an hour has 60 seconds in a minute and 60 minutes in an hour)

Thus, we get;

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3 years ago
the contractor demands a working temperature of 82 degrees Fahrenheit. what is the equivalent temperature in degrees Celsius
stiks02 [169]

Answer:

27.8 Celsius

Step-by-step explanation:

The equation to convert Fahrenheit and Celsius is:

F = (9/5)C + 32

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2 years ago
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Talja [164]
Salutations!

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Thus, your answer is option D.

Hope I helped :D
5 0
3 years ago
Read 2 more answers
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