4.
1 answer:
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Answer:
The required 97.5% confidence interval is
Therefore, we are 97.5% confident that the actual mean amount of juice in all such bottles is within the range of 15.19 to 15.81 ounces
.
Step-by-step explanation:
The amounts (in ounces) of juice in eight randomly selected juice bottles are:
15.8, 15.6, 15.1, 15.2, 15.1, 15.5, 15.9, 15.5
Let us first compute the mean and standard deviation of the given data.
Using Excel,
=AVERAGE(number1, number2,....)
The mean is found to be
=STDEV(number1, number2,....)
The standard deviation is found to be
The confidence interval for the mean amount of juice in all such bottles is given by
Where is the sample mean, n is the samplesize, s is the sample standard deviation and
is the t-score corresponding to a 97.5% confidence level.
The t-score corresponding to a 97.5% confidence level is
Significance level = α = 1 - 0.975 = 0.025/2 = 0.0125
Degree of freedom = n - 1 = 8 - 1 = 7
From the t-table at α = 0.0125 and DoF = 7
t-score = 2.8412
So the required 97.5% confidence interval is
Therefore, we are 97.5% confident that the actual mean amount of juice in all such bottles is within the range of 15.19 to 15.81 ounces.
