Mathematics: The length of a 95% confidence interval for mean Age is which of the following? (Because of potential roundoff, choose the closest.) Click here to reference the data needed to answer the question. a. 3.37 b. 3.72 c. 4.27 d. 3.11

The length of a 95% confidence interval for mean Age

alyssaarnold230

29.01.2022

The length of a 95% confidence interval for mean Age is 3.72.

Step-by-step explanation:

The data is provided for the age of 100 adults.

The mean and standard deviation are:

$\bar x=47.8\\\\s=9.3744$

As the sample size is too large the z-interval will be used for the 95% confidence interval for mean.

The critical value of z for 95% confidence level is, z = 1.96.

The length of a confidence interval is given by:

$\text{Length}=2\cdot z_{\alpha/2}\cdot\frac{s}{\sqrt{n}}$

$=2\times 1.96\times\frac{9.3744}{\sqrt{100}}\\\\=3.6747648\\\\\approx 3.67\\\\\approx 3.72$

Thus, the length of a 95% confidence interval for mean Age is 3.72.

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