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toyaluv2013
28.05.2020 •
Mathematics
The mean potassium content of a popular sports drink is listed as 145 mg in a 32-oz bottle. Analysis of 26 bottles indicates a sample mean of 144.4 mg. (a) State the hypotheses for a two-tailed test of the claimed potassium content. H0: μ = 145 mg vs. H1: μ ≠ 145 mg H0: μ ≤ 145 mg vs. H1: μ > 145 mg H0: μ ≥ 145 mg vs. H1: μ < 145 mg a b c (b) Assuming a known standard deviation of 2.9 mg, calculate the z test statistic to test the manufacturer’s claim. (Round your answer to 2 decimal places. A negative value should be indicated by a minus sign.) Test statistic (c) At the 10 percent level of significance (α = .10) does the sample contradict the manufacturer’s claim? Decision Rule: Reject H0 The sample the manufacturer's claim. (d) Find the p-value. (Round intermediate calculations to 2 decimal places. Round your answer to 4 decimal places.) p-value
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Ответ:
Step-by-step explanation:
Given that,
Sample size n= 26
Sample mean = 144.4mg
Population standard deviation = 2.9mg
a) Null and alternative hypothesis are
H₀ : μ = 145mg vs H₁ : μ ≠ 145mg
b) Test statistic is
c) the critical values at
Since it is two-tailed test
Decision rule: reject H₀
If Z > +1.645 or if Z < -1.645
Here Z = - 1.05 > - 1.645
⇒ we fail to reject H₀
⇒ the sample does not contradict the manufacturers claim
d) P-value = 2* P( Z < -1.05)
= 2 * 0.1469
= 0.2938
⇒ P-value = 0.2938
Ответ:
=48 hope this is what u needed
Step-by-step explanation: