Two sided
- Some people claim that they can tell the difference between a diet
soda and a regular soda in the first sip. A researcher wanting to test
this claim randomly sampled \(80\) such
people. He then filled \(80\) plain
white cups with soda, half diet and half regular through random
assignment, and asked each person to take one sip from their cup and
identify the soda as diet or regular. \(53\) participants correctly identified the
soda. Does this data provide strong evidence that people can tell the
difference between regular and diet soda? (when a significance level is
not specified use \(\alpha=.05\)).
\(H_0:\)
\(H_A:\)
- It is believed that \(40 \%\) of
people pass their driving test on the first attempt. Suppose you think
the percentage is different than \(40
\%\). So, you perform a hypothesis test and sample \(100\) people. Of the sampled people, \(43\) reply that they passed on their first
attempt. Set up a hypothesis test and make a conclusion with a \(10 \%\) significance level.
\(H_0:\)
\(H_A:\)
- A child is seeing how long they can hold their breathe under water.
The child thinks they can hold their breathe for \(150\) seconds on average. The child’s dad
thinks it less than that. He samples his daughter holding her breathe
eight times and the results are \(144\), \(152\), \(138\), \(144\), \(136\), \(162\), \(158\), and \(142\). From the perspective of the dad,
perform a hypothesis test using a \(5
\%\) level of significance. Does the data provide sufficient
evidence to reject the null hypothesis?
\(H_0:\)
\(H_A:\)
- Pew Research asked a random sample of \(1000\) American adults whether they
supported the increased usage of coal to produce energy. Their sample
showed that \(46 \%\) of support
increased coal usage. Set up hypotheses to evaluate whether a majority
of American adults support or oppose the increased usage of coal.
\(H_0:\)
\(H_A:\)
- You are given the following hypotheses:
\(H_0: \mu = 60\)
\(H_A: \mu \neq 60\)
We know that the sample standard deviation is \(8\) and the sample size is \(20\). For what sample mean would the \(p\)-value be equal to \(0.05\)?