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From a population with an unknown standard deviation, a simple random sample of size $100$ is taken.

The $t-$interval procedure will be used.

In this scenario, we may use the $t-$interval approach to determine the confidence interval of the population mean.

The sample size is $n=100$ here. As the sample size is more than $30$, it is a large sample. The population standard deviation $\mathrm{σ}$ is unknown.

Significant curvature can be seen in the normal probability plot. The population is therefore not normal; yet, because the sample is big, the sample mean $\stackrel{¯}{x}$ follows a normal distribution independent of the population distribution. In addition, the sample data contains no outliers. Unless the data contains outliers, the $t-$interval technique can be used for large samples. The employment of the $t-$interval technique is therefore justified.