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Answer:
We want to verify if young people today are waiting longer to get married (mean first married age is higher than 25.2 years) and that represent the alternative hypothesis, and the complement would represent the null hypothesis , the system of hypothesis then are:
Null hypothesis:[tex]\mu \leq 25.2[/tex]
Alternative hypothesis:[tex]\mu > 25.2[/tex]
Step-by-step explanation:
Info given by the problem
[tex]\bar X=27.5[/tex] represent the sample mean for the age of married men
[tex]s=4[/tex] represent the sample deviation
[tex]n=25[/tex] sample size selected
[tex]\mu_o =25.2[/tex] represent the value that we want to verify
How to create the system of hypothesis?
We want to verify if young people today are waiting longer to get married (mean first married age is higher than 25.2 years) and that represent the alternative hypothesis, and the complement would represent the null hypothesis , the system of hypothesis then are:
Null hypothesis:[tex]\mu \leq 25.2[/tex]
Alternative hypothesis:[tex]\mu > 25.2[/tex]
And in order to test this hypothesis we can use a one sample t test for the mean with the following statistic.
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Test claim is young people are waiting longer to get married [tex](\mu > 25.2)[/tex]
Test hypothesis:
A statistical hypothesis is an assumption about a population that may or may not be true. Hypothesis testing is a set of formal procedures used by statisticians to either accept or reject statistical hypotheses.
Null hypothesis is
[tex]H_0: \mu \le25.2[/tex]
Alternate hypothesis is
[tex]H_a: \mu > 25.2[/tex]
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