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A first-time convicted burglar spends an average of$2.5$ years in prison. The goal is to see if the average amount of time spent in prison has grown.

• The null hypothesis is
• $H_0$: A first-time convicted burglar spends less than or equal to $2.5$years in prison.
• The Null Hypothesis ($H_0$): It's a declaration that there's no difference between sample means or proportions, or between a sample mean or proportions and a population mean or proportion.

• The alternative hypothesis is:
• $H_a$: A first-time convicted burglar spends more than $2.5$years in jail on average.
• Here's an alternative theory: It is the population assertion that contradicts $H_0$, and it is what we conclude when we reject $H_0$.

For the above data, the null and alternative hypotheses are provided by:

$H_0:\mathrm{μ}≤2.5$

$H_a:\mathrm{μ}>2.5$