SKM_C300i-F24020713110

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Eastern Washington University *

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Feb 20, 2024

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N1 Togter W W 1. Sophia who took the Graduate Record Examination (GRE) scored 160 on the Ver- bal Reasoning section and W\o‘\ S 157 on the Quantitative Reasoning section. The mean score for Verbal Reasoning section for all test takers was pov b\"\\oti\\ 151 with a standard deviation of 7, and the mean score for the Quantitative Reasoning was 153 with a standard % deviation of 7.67. Suppose that both distributions are nearly normal. GRE SCORES _ ’w Verbal Quant z= o U 151 153 o 7 7.67 a. What is Sophia’s Z-score on the Verbal Reasoning section? On the Quantitative Reasoning section? ZNeoa\ = fi%—'—@ = L9 veroal \ ZQ;UC&V\“\ = Lfi_g-:é‘,fi/g_’_ -l 0.5 Q)UG\V\’(\"(G\*\\IC" b. What do these Z-scores tell you? ane &ored 1.2 stondenrd AN O DVS \M(%\A‘LY Haaw 0\\/e,r0\<‘(&e, 1w Vivioal e scorect 0,92 standarct deviarions W ner fiaan o\\lwo\%fi VA cU:an\-. c. Relative to others, which section did she do better on? Jevbo) , as swe scoved 1.29 grondard deviohious ooVt Yap Weon, compared vo onlyy 002 asvaudard deviahions above in qpavfinfa‘n\fit. d. What percent of the test takers did she perform better on the Verbal Reasoning section? On the Quantitative Reasoning section? ool 400 swe did otdier Yhaon quontkot Ve GA.98) ene Gid brtier than e. Sophia wants to increase her probabilities to obtain an academic scholarship and knows that scoring in the top 1% in verbal and in the top 5% in the quantitative sections will secure a scholarship from any top tier program. What are minimum scores for both sections that Sophia must attain? X 030 = X719 17,80 in verval 1 o =+ 'J 1 4o = 103 (R, 5% g0 AT AN E 7.6 -

BN ° 2. The US Preventive Services Task Force recently recommended that women under the age of 50 should not get routine mammogram screening for breast cancer. The Task Force argued that for a woman with a positive mammogram (one suggesting the presence of breast cancer), the chance that she has breast cancer was too low to justify a surgical biopsy. Suppose the table below represents a cohort of 100,000 women age 40 - 49 in whom mammogram screening and breast cancer behaves just like the larger population. For instance, in this table, the 3,333 women with breast cancer represent a rate of 1 in 30 women with undiagnosed cancer. The numbers in the table are realistic for US women in this age category. Monogram Result Breast Cancer Present Positive Negative Total Yes 3,296 37 3,333 No 8,313 88,354 96,667 Total 11,609 88,391 100,00 a. Does mammogram seem to be an accurate screening test in women who do have breast cancer? Justify your answer. - ) oot Coneer 3 jest 379 _—_"_’_____’_,4___——‘ VWAL CAMCEV ’_%)—é’%_'é—’ - Oq%O\ ov jfiq '/. Twis 18 oaw ‘oficc_ova*b Fest becaose iy 4esYs \005\‘\'\\‘13 fov 4897 of Loonmatn Pt acuplly Wadl cawcey b. The "[iask Force claims that if a woman between the ages of 40 and 49 tests positive for breast cancer, there is a low probability that she actually has breast cancer. We will then solve for the probability of cancer given a positive test using the table: q + " ot taucen 2 dest T 326 oo Egﬂ resty v 11604 8.4 ot ozt oo fest positiie, acwally noave COMCEY.

\U .9 3. Consider the following set of (sorted) observations and their summary statistics. Draw the boxplot below indicating the numerical values of all relevant markings. (8,10,11,15,15,17, 18,18 ,19, 19,19, 20, 20, 21, 23, 24, 25, 27 ,30 ,47] Min. :8.00 1st Qu.:16.50 Median :19.00 Mean :20.30 3rd Qu.:23.25 Max. :47.00 T0Q Q3- Ql L B0 1q 2515 30 2%.2%0 -5 a.15 =T wedigi Jovre R iSke~ OPpLr whiske—~ &l -TQR a’d +1Qe 105 - 675 2329 *+ -1 RN a. 75\ (50} Sl | WY 4, Aprofessor finds that the average SAT score among all students attending his college is 1150 £ 150 (it + G). He polls his class of 25 students and finds that the average SAT score is 1,200. Conduct a one-sample z test to determine whether the professor’s class SAT scores are larger (compared to the college mean SAT score) at a .05 level of significance? a. State the hypothesis Hop witown OAT SCOVES Sor fhw Clasd 19 o wost 1238 Yhan ov eqoal o Wik Mian AT score of IO (=150 Hi g o SAT SConS for ¥ cAOSE 15 %MW ot the o SR scove o W80 (> 1160) b. Set the criteria decision ( what is the critical value): FL0HD (one el ) ¢. Compute Z statistic O’M = o — 150 1606 A Tym s T 00 - 1200 ~W50 Z = M-~ 12807100 0™ o0

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d. Make a decision rejedh Bhe ol nupothesis e. Compute and interpret Cohen’sd = M M o—- -~ \206-1180 _ 5O E:j |60 1 50 =[0. %5 stodens Scoyed 0-33 svondard deyighions WQher faan 4 WeionQt average f. What is the confidence interval at 95% confidence? L rz (6F) 1200 T 16T (86 = |290. | 1200 = 107 (30)= 1149 .9 |e—— 07— 11499 12601 5. All human blood can be “ABO-typed”, i.e., be classified as being O, A, B or AB. The distribution of blood types varies across racial and ethnic backgrounds, however. The table below shows the probability of each of the blood types in China and the United States. Suppose that a couple made up of an American female and Chinese Male decide to marry, and individual blood type has not influence on their decision. o A B AB China 0.35 0.27 0.26 0.12 U.S. 0.45 0.40 0.11 0.14 a. What is the probability that they both have type AB blood? P(AVRY) = P(A)- P& = O,\’L - 0. 14 =[0.01® o 1. 687

b. What is the probability that they both have the same blood? (0.4 + O4L) + (04070 2) + (041 +D 2u)+ (014D $0.25) = 0.3104 31.09 /. Apple vs. FBI: Battle over unlocking phone. Survey USA asked 500 randomly sampled San Franciscans the following question "The FBI has a court order demanding Apple help it unlock the iPhone belonging to the San Bernardino shooter. Apple says creating the custom software this would require would set a dangerous precedence and create a back door that, in the wrong hands, could potentially be used to unlock ANY iPhone. Do you think Apple should? Or Should not? Comply with the court order in this particular case?" The distribution of responses by age group is shown below. Age Group 18-34 3549 50-64 65- [Total Should 64 55 88 65 272 Should not 50 51 35 22 158 Not sure 32 12 15 11 70 Total 146 118 138 98 500 (a) In evaluating the relationship between opinion on whether Apple should comply with the court order or not and age, what is the response variable and what is the explanatory variable? Explain your reasoning in one sentence. - Dependent: Opinion - Independent: Aoe - Explanation ( What is the relationship between the variables?) Mort \i\a_‘\fi Aok 0OE dedecmings opihion ow 4l iSS0e, not Hht otier woyy awoowd. (b) What are the cases in this study? B0 rvid oWl salecied Son FransiSCans (c) Suppose a statistically significant relationship is found between opinion on whether Apple should comply with the court order or not and age,to whom can the results be generalized? Al Sam FrowCiscoms ok \east 1® uars o\d (d) Does there appear to be a relationship between opinion on whether Apple should comply with the court order or not and age? Clearly state any probabilities you use as justification. 1%-24 — 2 457! 2% -4 —> 4T [ 80 - o4 —> b4 Y/ b~ — Lb. L twege proroae\nEs Ove difecent | there does appeor +o bE O veleionship ORIV ppivtion o whether Apple svputd oM Ply Wit e coovk prder oV not oand gL

(e) What is the probability that a randomly selected 18-34 year old believes that Apple should not comply with the court order? o _ . AN a Y Answer for the following questions. 1. Researchers studied 29,000 Finnish men, all smokers older than age 50. Half of the_a men,.selected at random, took vitamin supplements, and the other half took a dummy pill that has no active mgredient, The? researchers followed all the men for 8 years. At the end of the study, men in the vitamin group were no less likely to have cancer than men in the other group. 1W/ar is the independent variable? yivomin pdll 2. A researcher records the number of calories a person consumes per day and that person’s percent body fat. Whar is (are) the dependent variable(s)? pereedt vodu fad 3. A psychologist wants to know if adults with normal vision can be fooled by a certain optical illusion. She recruits 50 students with normal vision from her PSY 120 class and finds that 42 of them are fooled by the illusion. What was the psychologist’s sample? Sodevty withe o vision Multiple Choice Describe the shape of the sampling distribution of M, Approximately normal, because the sample size is sufficiently large. b. Approximately normal, because the sample mean is sufficiently large. ¢. Skewed right, because most babies in the sample will have a birth weight near 1000 grams. d. There is not enough information to tell. 2. Explain the difference between standard deviation and standard error. The standard deviation refers to the variability of a single random sample, and the standard error refers to the variability of a sample statistic from one random sample to the next. b. These are the same thing.

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¢. The standard error refers to the variability of a single random sample, and the standard deviation refers to the variability of a sample statistic from one random sample to the next. d. The standard deviation refers to the variability of all random samples, and the standard error refers to the variability of a population parameter from one random sample to the next. 3. True or false: Statistical significance means “the sample showed an effect larger than would often occur just by chance.” Statistical significance does not tell us whether an effect is large enough to be important. That is, statistical significance is not the same thing as practical significance. True b. False 4. What does the standard error estimate? a. The standard deviation of the distribution of a sample statistic b. The standard deviation of a population parameter ¢. The standard deviation of the entire population The standard deviation of the entire sample 5. Dogs have a very strong sense of smell and have been trained to sniff various objects to pick up different scents. An experiment was conducted with a dog in Japan who was trained to smell bowel cancer in stool samples. In a test, the dog was presented with five stool samples; one from a cancer patient and four from healthy people. The dog indicated which stool sample was from the cancer patient. This was repeated a total of 38 times. Out of the 38 tests, the dog correctly identified the cancer sample 37 times. A hypothesis test was conducted to see if this result could have happened by chance alone. The alternative hypothesis is that the dog correctly identifies cancer more than one-fifth of the time. The p-value is less than 0.001. Assuming this was a well-designed study, use a significance level of 0.05 to make a decision. Reject the null hypothesis and conclude that the dog correctly identifies cancer more than one fifth of the time. b. There is enough statistical evidence to prove that the dog correctly identifies cancer more than one fifth of the time. ¢. Do not reject the null hypothesis and conclude there is no evidence that the dog correctly identifies cancer more than one fifth of the time. 6. A hypothesis test has been conducted at the 0.05 significance level, resulting in a p-value of 0.25. Obviously, in this case, we would fail to reject Hy. If an error was made, it would be a(n): a. Typelerror. Type II error. ¢. Impossible outcome, since no error could have occurred with such a high p-value. 7. Does reading on a tablet or cellphone at bedtime increase how long it takes to fall asleep? A sample of 12 healthy adults slept in a lab on two different nights. In random order, participants read from a print book from 30 minutes before going to sleep or read on a tablet for 30 minutes before going to sleep. Scalp electrodes were used to measure how long (in minutes) it took participants to reach deep sleep with the tablet than the print book (p-value=0.009). Which is the best null hypothesis?

o Hy: The time it takes to fall asleep after reading on a tablet is the same as the time it takes to fall asleep after reading on a print book. b. Hy: The time it takes to fall asleep after reading on a tablet is greater than the time it takes to fall asleep after reading on a print book. €. Hy: The time it takes to fall asleep after reading on a tablet is less than the time it takes to fall asleep after reading on a print book. d. Hy: The time it takes to fall asleep after reading on a tablet is different than the time it takes to fall asleep after reading on a print book. 8. Ap-valueis: The probability of observing the actual result, a sample mean for example, or something more unusual just by chance if the null hypothesis is true. b. The probability that the null hypothesis is true. c. The probability of observing the actual result, a sample mean for example, or something more unusual just by chance if the null hypothesis is false. The t-distribution becomes less skewed as the sample size increases. e. The probability of observing the actual result, a sample mean for example. 9. A two-sided hypothesis test is used to determine whether the population parameter has Changed b. Increased c. Decreased d. Stayed the same 10. A one-sided hypothesis test is used to determine whether the population parameter has Either increased or decreased (depending on the research question) b. Increased ¢. Decreased d. Either increased or decreased (depending on the null hypothesis) 11. Rejecting the null hypothesis when the null hypothesis is true is called a: Type 1 Error b. Type 2 Error ¢. Type 3 Error d. Correct decision 12. Failing to reject the null hypothesis when the null hypothesis is false is called a Type 2 Error b. Type 1 Error c. Type 3 Error d. Correct decision 13. Breastfeeding mothers secrete calcium into their milk. Some of this calcium may come from thei it thought that nursing mothers will lose ! e bone mineral content. Researchers compared 47 breastfeeding mothers

with 21 women of similar ages who were neither breastfeeding nor pregnant. They measured the mineral content of the women’s spines over three months. A negative value indicates a loss in mineral content. 0.20 - [ 0.15 — | - =2 f 2 | 3 0.10 — r- — 0.05 - , | | 0.00 ko — L = | | i 1 ] I I -8 -6 -4 2 0 2 Control Choose the best description of the distribution of change in bone mineral content for the control group. The distribution is roughly left skewed and unimodal, and centered around -1. b. The distribution is roughly symmetric and unimodal, and centered around 0. ¢. The distribution is roughly right skewed and unimodal, and centered around -1. d. The distribution is roughly uniform and centered around -2. 14. The larger the sample, the accurate the sample statistic will be as an estimate of the population parameter. ¢. Can’t say because sample size doesn’t affect accuracy of an estimate d. Can’t say because it depends on the exact sample values

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SKM_C300i-F24020713110

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