Use the given degree of confidence and sample data to construct a confidence interval for the population mean mu μ. Assume that the population has a normal distribution. A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with s equals =17.6 milligrams. Construct a​ 95% confidence interval for the true mean cholesterol content of all such eggs A. 175.9 mg less than < mu μ less than <194.1 mg
B. 173.9 mg less than < mu μ less than <196.1 mg
C. 173.8 mg less than < mu μ less than <196.2 mg
D. 173.7 mg less than < mu μ less than <196.3 mg

Answer:

option (C) 173.8 mg less than < mu μ less than <196.2 mg

Step-by-step explanation:

Data provided ;

number of sample, n = 12

Mean = 185 milligram

standard deviation, s = 17.6 milligrams

confidence level = 95%

α = 0.05                                     [for 95% confidence level]

df = n - 1 = 12 - 1 = 11

Now,

Confidence interval = Mean ± E

here,

E is the margin of error =

also,

=    

=   2.201                         [ from standard t value table]

Thus,

E =

or

E = 11.182 milligrams ≈ 11.2 milligrams

Therefore,

Confidence interval:

Mean - E < μ < Mean + E

or

185 - 11.2 < μ < 185 + 11.2

or

173.8 < μ < 196.2

Hence,

the correct answer is option (C) 173.8 mg less than < mu μ less than <196.2 mg

Final answer:

To construct a confidenceinterval for the population mean cholesterol content of all chicken eggs with a 95% confidence level, we use the sample mean, standard deviation, and sample size to calculate the margin of error. The confidence interval is then constructed by subtracting the margin of error from the sample mean and adding it to the sample mean.

Explanation:

To construct a confidenceinterval for the population mean cholesterol content of all chicken eggs, we first need to find the margin of error. The margin of error depends on the samplemean, standard deviation, sample size, and the desired level of confidence. In this case, we have a sample mean of 185 mg, a standard deviation of 17.6 mg, and a sample size of 12. Since we want a 95% confidence interval, we use a z-score of 1.96. The margin of error is then calculated as 1.96 * (17.6/sqrt(12)), which is approximately 9.61 mg. We can then construct the confidenceinterval by subtracting the margin of error from the sample mean and adding it to the sample mean. Therefore, the 95% confidence interval for the true mean cholesterol content of all such eggs is 175.9 mg to 194.1 mg.

Learn more about Constructing confidence intervals here:

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