Q 8.13RP. - Elementary Statistics

Question

A random sample of size $50$ is taken from a population. A boxplot of the sample data reveals no outliers. 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 $50-$person random sample is chosen from a population. There are no outliers in the sample data, according to a boxplot.

Step 2: Concept

The formula used: $z-$interval procedure and $t-$interval procedure 

Step 3: Explanation

Determine whether the $z-$interval process, the $t-$interval procedure, or neither is the best way for generating the confidence interval.

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

The sample size is small:

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:

Sample size is small:

- 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 large sample size of $(=50)$ 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 create a confidence interval for the population mean is clearly appropriate given the aforesaid parameters.