Q 8.16RP. - Elementary Statistics

Question

A random sample of size $128$ is taken from a population. A normal probability plot of the sample data shows no outliers but has significant curvature. The population standard deviation is known.

Step-by-Step Solution

Answer

It is clear that the applying $z-$interval procedure to obtain a confidence interval for the population mean is appropriate.

Step 1: Given information

A population is sampled with a $128-$person random sample. The sample data displays significant curvature but no outliers on a normal probability curve.

Step 2: Concept

The formula used: is the $z-$interval procedure.

Step 3: Explanation

Check whether the $z-$interval process, the $t-$interval procedure, or neither is the best approach for determining the confidence interval.

The following are the conditions for using the $z-$interval procedure:

Small Sample size:

When the sample size is less than $15$, and the variable is normally distributed or extremely close to being normally distributed, the $z-$interval technique is utilized.

Moderate Sample size:

When the sample size is between $15$ and $30$, and the variable is not normally distributed or there is no outlier in the data, the $z-$interval technique is performed.

Large Sample size:

The $z-$interval technique is utilized without restriction if the sample size is bigger than 30.

Step 4: Explanation

The following are the conditions for using the $t-$interval procedure:

Small Sample size:

• From the population, samples are drawn at random.
• The sample size is higher or the population follows a normal distribution.
• The standard deviation has not been determined.

The sample is drawn from the population, with a huge sample size of $(=128)$

Furthermore, the population standard deviation is known, and no outlier exists. As a result, the variable's distribution is roughly normal. The application of the $z-$interval approach to creating a confidence interval for the population mean is clearly appropriate given the preceding criteria.