Find the value of the test statistic for hypothesis testing on proportions

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to find the value of the test statistic for hypothesis testing on proportions.  Here's our problem statement: Claim: Most adults would erase all of their personal information online if they could.  A software firm survey of 591 randomly selected adults showed that 60% of them would erase all their personal information online if they could.  Find the value of the test statistic.

Solution

OK, we could go old school and drag out this.  It's not really complicated, but it's a formula that requires a little bit of work.  I'm lazy; I don't want to do that kind of thing, so I'm gonna use technology to get my test statistic.  And specifically I'm gonna use StatCrunch.  So here I have pulled up here in a separate window StatCrunch.  Notice there's no icon here that I can click to get the StatCrunch to show up.  So oftentimes when I work these homework problems, I find it helpful to just keep StatCrunch open in a separate window just in case I need it.  And this is a good case in point.  I can use StatCrunch to get what I'm looking for, and I can avoid that nasty old-school calculation.

So here we are in StatCrunch.  First, I'm going to click on Stat; go down to Proportion Stats, because we're dealing with proportions; One Sample because we only have one sample; and then With Summary because we don't have actual data, just some summary stats.

Here in the options window, the first thing I'm asked to do is calculate the number of successes.  I can get this from the problem statement.  It said 60% of the people would erase all their personal information online if they could.  I know the total — 591 — so all I need to do is a little calculation.  So in my calculator, I'm gonna put 60% times the total 591.  That gives me the proportion I'm looking for — 354.6.  We want a whole number, because there's no such thing — well, there could be such a thing as six tenths of a person, but it wouldn’t do anybody any good.  So let's only count whole people.  We're gonna round this to the nearest whole number.  So that would be 355.

Then the total number of observations — the total from the survey, 591 — and then we don't need to mess with any of these other settings because the default values will serve us for what we need.  All we want is the test statistic.  So these values here are more for determining the P-value than the test statistic.  We don't want the P-value, just the test statistics, so these default values are fine for us.  I click Compute!, and then here in my results window, we see right here towards the end of the table our test statistic.  I'm asked around the two decimal places.  Well done!

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