Question

1. A researcher believes that university students weigh more than the population. The researcher reasons that more time spent on studying for exams means having less time to exercise. The researcher selects an alpha level of 0.10 (or CL = 90%). Upon looking at census data, the average American weighs 170lbs with a standard deviation of 35lbs.
The researcher takes a random sample of 225 CSU students and finds that the mean weight of CSU students is 180lbs with a sample standard deviation of 45.

Is there enough evidence to reject the null hypothesis?

Answer 1

Answer:

The null and alternative hypotheses are:

$H_{0}: \mu = 170$

$H_{a}: \mu >170$

Under the null hypothesis, the test statistic is:

$z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}} }$

         $=\frac{180-170}{\frac{35}{\sqrt{225}} }$

         $=\frac{10}{2.33}$

         $=4.29$

Now, we have to find the right tailed z critical value at 0.10 significance level. Using the standard normal table, we have:

$z_{critical} = 1.28$

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.