# Multiple choice Prep

#### StatsH

##### New Member
Hey,
I was wondering if anyone could help me prep for my upcoming test by helping me with these questions I got of a statistics site:

1. In class B.J and Tony were performing a hypothesis test. Both received the same test stat, but B.J’s result was to reject the null hypothesis while Tony’s result was not to reject it. Which is not a possible explanation for why they had different conclusions:

- B.J performed an upper – tail test while Mike performed a lower-tail test
- B.J was performing a one-tail test and Tony was performing a two tail one
- B.J considered the test stat to be z while Tony considered the test stat to be t
- B.J was testing at the 0.1 significance level while Tony was testing at a .05 level
- B.J computed the p-value of the test statistic while Mike compared the test statistic to the corresponding critical value for the t-table of critical values.

I think that I eliminated 4th one and 2nd one, but I don't know about the rest.

2) muA = the mean ACT writing score
muB = the mean of ACT writing score of students who took the practice test
The 99% confidence for the true mean difference between the two means is (2,5). Which statement is the best interpretation of this confidence interval?

- uB – uA with probability 0.99
- It’s likely that the difference uB – uA will exceed 5
- With probability 0.99, the interval (2,5) contains the true difference uB-uA
- uB is about equal to 5, and uA is about equal to 2
- uB – uA is about equal to 3

For this, I think I narrowed it down to the last choice and the 3rd one. I'm not sure if it's one of those or not

Thanks a lot #### StatsH

##### New Member

1 ) B.J performed an upper–tail test while Mike performed a lower-tail test.
It wouldn't matter if it was an upper or lower one right? They'd still have
to have the same probabilities.

2) With probability 0.99, the interval (2,5) contains the true difference uB-uA
I know this confidence level means that they are 99% confident that the
mean difference is from 2 to 5. Does this correspond to the "probability"
also?

Those are my "educated" guesses at best. Can someone explain/correct me?
Thanks #### Mean Joe

##### TS Contributor
Hey,
I was wondering if anyone could help me prep for my upcoming test by helping me with these questions I got of a statistics site:

1. In class B.J and Tony were performing a hypothesis test. Both received the same test stat, but B.J’s result was to reject the null hypothesis while Tony’s result was not to reject it. Which is not a possible explanation for why they had different conclusions:
A point of absolutely no consequence: Problem above states the names BJ and Tony, then the answer choices introduce a Mike.

- B.J performed an upper – tail test while Mike performed a lower-tail test
This is a possibility. Let's say the test statistic is z=1.8. In an upper-tail test, BJ would reject if z > 1.645, while Tony would reject if z < -1.645. Thus, it's possible that BJ would reject while Tony wouldn't.

- B.J was performing a one-tail test and Tony was performing a two tail one
This is a possibility. BJ would reject if z > 1.645, while Tony would reject if |z| > 1.96. If z was 1.8, then BJ could reject when Tony doesn't.

- B.J considered the test stat to be z while Tony considered the test stat to be t
This is a possibility. The critical value in a z-test is lower than the critical value in a t-test. A test is rejected if the statistic exceeds the critical value. Thus, it's possible that the statistic exceeds BJ's lower z-test critical value, but not Tony's higher t-test critical value.

- B.J was testing at the 0.1 significance level while Tony was testing at a .05 level
This is a possibility. The critical value at the 0.1 significance level is lower than the critical value at the 0.05 level.

- B.J computed the p-value of the test statistic while Mike compared the test statistic to the corresponding critical value for the t-table of critical values.
Doing either method, you should come to the same conclusion. e.g. if z=1.8 and you want to do BJ's method, then the p-value is .0359 (so you would reject at a=.05 level); and if you do Tony's method, then the critical value you find is z[a]=1.645 (so you would reject). I know it says t-table above, but the logic is the same.

2) muA = the mean ACT writing score
muB = the mean of ACT writing score of students who took the practice test
The 99% confidence for the true mean difference between the two means is (2,5). Which statement is the best interpretation of this confidence interval?
- With probability 0.99, the interval (2,5) contains the true difference uB-uA