Answer:
The null and alternative hypotheses are:
[tex]H_{0}: \mu = 170[/tex]
[tex]H_{a}: \mu >170[/tex]
Under the null hypothesis, the test statistic is:
[tex]z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
[tex]=\frac{180-170}{\frac{35}{\sqrt{225}} }[/tex]
[tex]=\frac{10}{2.33}[/tex]
[tex]=4.29[/tex]
Now, we have to find the right tailed z critical value at 0.10 significance level. Using the standard normal table, we have:
[tex]z_{critical} = 1.28[/tex]
Since the test statistic is greater than the z critical value, we therefore, reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the university students weigh more than the population.
