Q 8.12RP. - Elementary Statistics

Question

A random sample of size $17$is taken from a population. A normal probability plot of the sample data is found to be very close to linear (straight line). The population standard deviation is unknown.

Step-by-Step Solution

Answer

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

Step 1: Given information

A $17$-person's random sample is collected from a population. The sample data's normal probability plot is determined to be very close to linear (straight line).

Step 2: Concept

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

Step 3: Explanation

Check whether the $z-$interval process, the $t-$interval procedure, or neither is the best way 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 has a regularly distributed or nearly normal distribution, the $z-$interval technique is used.

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:

The 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 size is minimal and the sample is drawn from the population. Furthermore, the standard deviation of the population is unknown. The application of the $t-$interval approach to creating a confidence interval for the population mean is clearly appropriate given the preceding parameters.