this question involves language about 'rejecting the null hypothesis'; that language is 'old' and is based on using a significance level to draw conclusions from a hypothesis test. While we don't focus on this language anymore in our course, it's still good to think about what it means. So, use this practice question to test your understanding of hypothesis testing in general (even though you won't see "reject the null hypothesis", etc. on your exam).

The "Dream Lottery" raises money for hospitals and care centres in London by selling lottery tickets for several Dream Homes. Winners can accept the home, or, $1 million cash instead.

Your instructor purchases a couple of tickets. She is convinced the true mean value of the homes offered by the Dream Lottery is more than $1 million; therefore, accepting the home is the better deal if she wins. To test this, she will collect the actual home values of a simple random sample of homes from the Dream Lottery websites. She will conduct the appropriate hypothesis test,exceptshe has made a mistake in deciding whether the test should be one-tailed or two-tailed.

Which of the following statements correctly reflects aconsequenceof this mistake?

• A.She will have increased the risk of rejecting the null hypothesis when it should not have been rejected.
• B.She will have decreased the standardized version of her sample mean of home values.
• C.She will have decreased the probability of getting mean home values as extreme or more extreme than her sample mean of home values.
• D.She will have increased the degree of extremeness for a sample mean of home values that would be needed to result in a rejection of her null hypothesis.