The inspection division of the Lee County Weights and Measures Department is interested in determining whether the proper amount of soft drink has been placed in 2-liter bottles at the local bottling...

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The inspection division of the Lee County Weights and Measures Department is interested in determining whether the proper amount of soft drink has been placed in 2-liter bottles at the local bottling plant of a large nationally known soft-drink company. The bottling plant has informed the inspection division that the standard deviation for 2-liter bottles is 0.05 liter. A random sample of 100 2-liter bottles selected from this bottling plant indicates a sample mean of 1.99 liters.

a. At the 0.05 level of significance, is there evidence that the population mean amount in the bottles is different from 2.0 liters?

b. Compute the p-value and interpret its meaning.

c. Construct a 95% confidence interval estimate of the population mean amount in the bottles.

d. Compare the results of (a) and (c). What conclusions do you reach?

Answered Same DayDec 25, 2021

Answer To: The inspection division of the Lee County Weights and Measures Department is interested in...

Robert answered on Dec 25 2021

116 Votes

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A Test: µ 6= 2 with normal distn
Hypothesis test:
H0 : µ = 2 (Null Hypothesis)
Ha : µ 6= 2 (Alternative Hypothesis, also called H1)
This is two tailed test.
x = 1.99
σ = 0.05
n = 100
Significance Level, α = 0.05
Test statistic z? = x− µ
σ/
√
n
Test Statistic, z? = 1.99− 2
0.05/
√
100
= −2.00
Test Statistic, z? = −2.00
The Critical Value = zcrit = zα/2 = z0.025 =1.96 (From z table)
Critical Values ±1.96
Rejection Rule: Reject H0 if |z?| > zc (because this is 2 tailed test)
Rejection region has been shaded:
α/2 = 0.025
−zα/2 = −1.96
0
α/2 = 0.025
zα/2 = 1.96
Decision: Since | − 2.00| > 1.96, we reject the null hypothesis.
Hence at 5% significance level, we have sufficient evidence to conclude that µ
is different from 2
We have sufficient evidence that population mean amount in the bottles is
different from 2.0 liters
X
B P-value...

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