Question

Asked Apr 24, 2019

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Step 1

**Obtain the critical value:**

The required confidence level is 100*(1–α)% = 95%.

The required conditions for using *t *distribution to estimate the confidence interval about mean is given below:

- The population standard deviation σ must be unknown.
- Either the sample size (
*n*) must be greater than 30 or the population must be normally distributed.

Here, the sample size is *n *= 300 (which is greater than 30) and the population standard deviation is unknown.

The critical value is obtained as 1.968 from the calculation given below:

Step 2

**a.**

**Find the margin of error of the confidence interval with 95% confidence level:**

Given that, the sample standard deviation is *s* = $15,

The sample mean is *x*-bar = $23,

The sample size is *n *= 300,

The critical value is *t*_{(}_{α/2, n–1)} = *t*_{0.025,299} = 1.968.

The margin of error of the confidence interval with 95% confidence level is obtained as **1.7043** from the calculation given below:

Step 3

**b.**

**Interpretation of margin of error:**

The margin of error gives the accuracy of the estimate. It says the error for the statistic to be parameter.

Here, the margin of error is *E *= 1.7043.

From this it can be said that, we are 95% confident t...

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