Test 11B AP Statistics Directions: Work on these sheets. Tables and formulas appear on a separate sheet.

) nsvec Name: K-2_

Part 1: Multiple Choice. Circle the letter corresponding to the best answer

1. The average time it takes for a person to experience pain relief from aspirin is 25 minutes. A new ingredient is added to help speed up relief. Letµ denote the average time to obtain pain relief with the new product. An experiment is conducted to verify if the new product is better. What are the null and alternative hypotheses? @ Ho:u=25 vs.H,:u +25 //, L= 25S (b'Ho:=25 vs. H,:<25 '9 (©) Ho:<25vs.H,:u=25 /4, M <25y (d) Ho: <25 vs. H,: > 25 (e) Ho: =25 vs. H,: > 25

2. A significance test was performed to test the null hypothesis H,: =.2 versus the alternative H,: > 2. The test statistic is z = 1.40. The P-value for this test is approximately (a) 0.16 ((@ o.0s (c) 0.003 (d) 0.92 (e) 0.70 (f) None of the above. The answer is _

.0808

3. Ina test of Hy: = 100 against H,: 100, a sample of size 10 produces a sample mean of 103 and a P-value of 0.08. Thus, at the 0.05 level of significance (a) there is sufficient evidence to conclude that p ± 100. (b) there is sufficient evidence to conclude that = 100. (c) there is insufficient evidence to conclude that = 100. ((d) there is insufficient evidence to conclude that ± 100. ( e) there is sufficient evidence to conclude that µ = 103.

X= 1o3 \= 1O P>.0% Po>,06 Vpi Es ( t.­

4. To determine the reliability of experts used in interpreting the results of polygraph examinations in criminal investigations, 280 cases were studied. The results were 9 ks( T'rue Status • cl /r{{

Innocent .G~stf .)_L'tl' · .. • · ~-~, 1 1,1<1 131 l_J G~• i,-Jr·\ tJ\'-'1 < hf • 9 1254-te jo (\yy?

If the hypotheses were Ho: suspect is innocent vs. H,: suspect is guilty, then we could estimate the probability of making a Type II error as (a) 15/280 (b) 9/280 (©))15/140 (@j 9/140 (e) 15/146

Examiner's Decision

"Innocent" "Guilty"

Chapter II Test l lB

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5. A certain population follows a Normal distribution with mean u and standard deviation .9y o =2.5.You collect data and test the hypotheses > { (f'%j

H,:u=\,H,:u#1 You obtain a P-value of 0.022. Which of the following is true? .DJ< c; 5.io (a) A 95% confidence interval for will include the value 1. ] \ / (b) A 95% confidence interval for will include the value.0. A' 1 ((c))A 99% confidence interval for will include the value 1. (@y A 99% confidence interval for will include the value0. -oD. ¢ (e) None of these is necessarily true. > 9\Joi/t Altew.f ,°

inst@ 44, 6. Vigorous exercise helps people live several years longer (on the average). Whether mild activities

like slow walking extend life is not clear. Suppose that the added life expectancy from regular slow walking is just 2 months. A statistical test is more likely to find a significant increase in mean life if ((a)it is based on a very large random sample and a 5% significance level is used. -/'3 , (b6) it is based on a very large random sample and a 1% significance level is used. _(1_ _DK (c) it is based on a very small random sample and a 5% significance level is used. "- :h ,- (d) it is based on a very small random sample and a 1% significance level is used._>>/ " (e) The size of the sample doesn't have any effect on the significance ofthe test. t{_

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7. Which of the following is not a condition for performing inference about a population mean ? (a) Inference is based on n independent measurements. (b) The population distribution is Normal or the sample size is large (say n> 30). ( c) To use a z test, we must know the population standard deviation a . · d, he data are obtained from an SRS from the population of interest.

oth np and n(l- p) are 10 or greater. ··~ , .

8. Does taking ginkgo tablets twice a day provide significant improvement in mental performance? To investigate this issue, a researcher conducted a study with 150 adult subjects who took ginkgo tablets twice a day for a period of six months. At the end of the study, 200 variables related to the j\ y mental performance of the subjects were measured on each subject and the means compared to {\JF ,,9(°' known means for these variables in the population of all adults. Nine of these variables were,/r?q', significantly better(in the sense of statistical significance)at the z =0.05level forthe group-,\90 ( .«S taking the ginkgo tablets as compared to the population as a whole, and one variable was \h ,cc»' significantly better at the z =0.01level for the group taking the ginkgo tablets as compared to the{\\.{'

<, population as a whole. It would be correct to conclude that 2r g!· ' }O\ (a) there is very good statistical evidence that taking ginkgo tablets twice aday provides some\ ;_[o+

I ~ , c, ~ improvement in mental performance. \;''\ ' ',(b) there is very good statistical evidence that taking ginkgo tablets twice a day provides )'.)° improvement for the variable that was significant at the z =0.01 level. We should be cautious

/ ~ ') · ,J, about making claims for the variables that were significant at the c =0.05 level. ,O',,0° (c) these results would have provided very good statistical evidence that taking ginkgo tablets X yO twice a day provides some improvement in mental performance if the number of subjects had 'V,,, been larger. It is premature to draw statistical conclusions from studies in which the number of

~'c§ ~y--- subjects is less than the number of variables measured. , ~ ( d) there is very good statistical evidence that taking ginkgo tablets twice a day provides significant

~ improvement in ten specific areas related to mental condition., \(©)/one of the above ,\up@ Gt yla ®sf(¢

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Test 12D AP Statistics Name: Directions: Work on these sheets. Answer completely, but be concise. Tables are attached

Part 1: Multiple Choice. Circle the letter corresponding to the best answer.

1. An opinion poll asks a simple random sample of 100 college seniors how they view their job prospects. In all, 53 say "good." Does the poll give reason to conclude that more than half of all seniors think their job prospects are good? The hypotheses for a test to answer this question are @cp=05.H;>0.5. 7) Hr p> 0.5,Hp =0.5. (c) Ho. p =0.5, Hp ± 0.5. (d) Hy. p=0.5, H,:p <0.5. (e) Ho: p 0.5,H4. p> 0.5.

The next two questions refer to the following situation. A group of nutritionists is hoping to prove that a new soybean compound has more protein per gram than roast beef, which has a mean protein content of 20. A random sample of 5 batches of the soy compound have been tested, with the following results:

protein content 15, 22, 17, 18, 23

2. What assumption( s) do we have to make in order to carry out a legitimate statistical test of the nutritionists' claim? (a))The observations are from a Normally distributed population. '() The mean protein content of the 5 batches follows a Normal distribution. ( c) The variance of the population is known. (d) Both (a) and (b) must be assumed. ( e) All of (a), (b ), and ( c) must be assumed.

3. What are the appropriate statistical hypotheses and the observed value of the corresponding test statistic? (a) Ho: =20 vs. H; <20 and z'= (19--20)//11.5/5 (@t; =20 vs. H: > 20 and/'= (t9-20)//f1.57s (c) Ho: =20 vs. H;: > 20 and z'= (19-20)//11.5/5 (d) He: =20 vs. H: <20 and z'= (19-20)//11.5/5 (e) None of these is correct.

4. Ina test of Hy: p=0.4 against H,: p ± 0.4, a sample of size 100 produces z= 1.28 for the value of the test statistic. Thus, the P-value (or observed level of significance) of the test is approximately equal to: (a) 0.90 (b) 0.40

0.05 0.20 0.10

Chapter 12 1 Test 12D

5. The infamous researcher, Dr. Gnirips, claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Ten people are randomly selected from students at Brandon, their heights measured, the drug administered, and 2 hours later their heights remeasured. The results were as follows:

Pre-Drug 68 Post-Drug 70 Person 1

69 69 2

74 75 3

78 78 4

70 73 5

66 69 6

71 72 7

70 73 8

71 72 9

65 66 10

Using the proper test statistic, an appropriate decision rule for the hypotheses Hy: Drug has no effect versus H,: Drug increases height at z =0.05 will be (a) Reject Ho if the test statistic is> 1.96 (b) Reject Ho if the test statistic is > 1.645 ((c)'Reject Ho if the test statistic is> 1.833 ( d) Reject Ho if the test statistic is > 1. 73 (e) Reject Ho if the test statistic is> 2.10

6. Refer to the previous question. The power of the test to detect an average increase in height of one inch could be increased by (a) using only members of the basketball team in the experiment. (b) using a = 0.01 instead of a = 0.05. (c) giving the drug to one group of 10 students and using another group of 10 students for control.

((d)giving the drug to 20 randomly selected students instead of 10. (e) using a z test instead of a t test.

7. You have data on rainwater collected at 16 locations in the Adirondack Mountains of New York State. One measurement is the acidity of the water, measured by pH on a scale of Oto 14 (the pH of distilled water is 7.0). Which inference procedure would you use to estimate the average acidity of rainwater in the Adirondacks? (a) one-sample z interval for µ (b)one-sample t interval for p (c) paired t test ( d) one-sample t test ( e) one-sample z test

8. Which of the following is not a correct statement about conditions for performing a significance test about an unknown population proportion p? (a) The data should come from a randomized experiment or simple random sample. Individual measurements should be independent of one another.

The population distribution should be approximately Normal, unless the sample size is large. ) Both np and n(l -p) should be at least 10.

( e) If you are sampling without replacement from a finite population, then you should sample no more than 10% of the population.

Chapter 12 2 Test 12D