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 mean 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?
or do not h0. the sample or does not 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)?

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, = 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

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

b) Formula:

Putting all the values, we have

c) Now,

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.

answer:

given the linear inequality :

add 2y to both sides we get;

simplify:

add 12 to both sides of an equation;

simplify:

divide both sides by 2 we get;

or

the related equation for the inequality equation [1] is;

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

subtract 6 from both sides we get

multiply both sides by 2 we get;

or

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.