# Thread: Determining Null and Alternative Hypothesis for directional Hypothesis testing

1. ## Determining Null and Alternative Hypothesis for directional Hypothesis testing

So I have been reading notes and been doing exercises on the hypothesis testing and now I understand how to implement
the systematic steps of the testing.

I still don't understand when I have a directional case what my hypotheses should be.
I came across the following question

Verify a claim that the average amount of time spent by high school students on console games is 300 minutes. A sample of 30 indicates that the average amount of time spent is 317 min and the population standard deviation is 42.50 minutes. At the 0.05 level of significance, conduct a hypothesis test to determine if the true mean time spent is greater than 300 minutes.

Now, I'm really confused. I think the research question seems to imply we should have H0: u = 300. But what about the last setence where u >30 ? where should that come in?

Help will be appreciated. Thank you.

2. ## Re: Determining Null and Alternative Hypothesis for directional Hypothesis testing

The null hypothesis is that $u=300$ min. You are to construct a (one sided) test for this which if $u=300$ will be passed 95% of the time. In this case the critical value will be $1.65$ standard errors above the null hypothesis mean. The standard error for a sample size of 30 is $s/\sqrt{30}$ and we estimate the standard deviation $s$ with the population standard deviation estimate from the sample so the critical value for the test is $300+1.65 \times 42.5/\sqrt{30}=312.8$. So in this case our test leads us to reject the null hypothesis.

We would describe this test result as showing that the mean time spent on console games by high school students is significantly greater than $300$ min at a 5% level of significance.

The problem here is that the original question "Verify a claim that the average amount of time spent by high school students on console games is 300 minutes" implies a 2-sided test (1.96 standard errors). What we have done is answer the different question at the end "conduct a hypothesis test to determine if the true mean time spent is greater than 300 minutes". The problem is that there is a conflict in what you are being asked to do.

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3. ## Re: Determining Null and Alternative Hypothesis for directional Hypothesis testing

I thought that the critical t depends on your alternative hypothesis. So if u were state the Null and Alternative what would they be?

4. ## Re: Determining Null and Alternative Hypothesis for directional Hypothesis testing

H0: $u=300$
H1: $u>300$