Review #3

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Northern Arizona University *

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Electrical Engineering

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Feb 20, 2024

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Uploaded by GrandGoose2784

Review #3 1. The following figure shows a randomization distribution for the hypotheses Hy -4 =#2 versus H,, : ) # u5. The statistic used for each sample isD= \‘| - .\';» Which of the two possible sample results provides the most evidence against Ho? r——]j 60 4 4‘1 | 20 ’ ” = = 565 _S1:.3= 52 @\'1=565' x5 =513 b ﬂ/ - =, = 6°:2 c L= B)¥; =502; X, =53.1 v A L mve edfreme €V“lm(€ Ct'zj*zuﬂl{ He - 2. Identify the error in the following hypotheses: Frequency ] n/’f’ J'i‘\’/” e =] ~ | Ao )'-\) ava- S a) Hy:p 0.75 versus H‘, p> 0.75. 7. “+ ’ > lww A‘,’-'t'»—m; ove cduways ol e ST Voo camge ctakichi'es ' b) Hy:u# 56 versus H, :u = 56. mtr ol i egue L;;f"/ tudf '.,,(&‘\,;« 5 15 alb®ys A ¢) Hy:p=30versus H,:p>30 /( zimg weare -ﬂ;rbn'lon l\\ouli be beloeen © “"“ _’ 3. Of the two p-values, which provides more evidence against /? i. p-value=0.02 ii. p-value=0.007>

4. Use the following to answer the questions below: Consider testing the hypotheses H;, : p = 0.4 versus H, : p > 0.4. Four possible sample statistics, along with four possible p-values, are given. Match the statistics to their p-values. A.p=042 B.p=038 C.p=051 D.p=046 " a) 09 B p-value = 0.72 b) O'42 p.value=0.293 / c) oo p-value = 0.138 N - i = f d) D5 p-value=0.019 e 2" 5 f,( 042 Y4 5. A Type I error occurs by a) rejecting the null hypothesis when the null hypothesis is false. b) not rejecting the null hypothesis when the null hypothesis is false. (’a) rejecting the null hypothesis when the null hypothesis is true. ) not rejecting the null hypothesis when the null hypothesis is true. 6. A Type II error occurs by rejecting the null hypothesis when the null hypothesis is false. C;)) not rejecting the null hypothesis when the null hypothesis is false. c) rejecting the null hypothesis when the null hypothesis is true. d) not rejecting the null hypothesis when the null hypothesis is true. 7. Decreasing the significance level of a hypothesis test (say, from 5% to 1%) will cause the probability of making a Type I error to a) increase. @ decrease. CJ stay the same. 8. Using a significance level of 5%, What would be the approprmu conclusion for a test with a p-value of 0.0421? ’ Sl (:1-—!-:-[- A e have

1t is believed that about 37% of college students binge drink (5 or more drinks for men, and 4 or more drinks for women, in two hours). Administrators at a small university of 6,000 students want to do a study to determine if the proportion of their students who binge drink differs from 37%. They select a sample of 98 students enrolled at the university to survey about their drinking behavior. When generating the randomization distribution for this test, how large should each individual randomization sample be? ! G wdithid vandomizdon songle gladd be 8 as we e S2e. 10. In an experiment, students were given words to memorize, then were randomly assigned to take a 90-minute nap or take a caffeine pill. They were then tested on their recall ability. We test o see if the sample provides evidence that there is a difference in mean number of words people can recall depending on whether they take a nap or have some caffeine. a) Write down the hypotheses. My e te Mec w Mean ne w )y pefle con el dhondecy bbe < nop A v R (R RD ,ka‘rilr\é X Mn= Mc M o Sl i ta: MAn % L b) The sample statistic is 3.0.Use the randomization distribution to state the p-value. Randomization Dotplot of = ; — T 2; Null hypothesis sy o 1 Left Tait [¥] Two-Tait [Tl Right Tait 4 samples — 1000 mean 0.021 st. dew. 1.499 0.022 ¢) State the formal conclusion. P’\«i"‘(’ (604 A%(r .Y ) hence we rejedt Hee nw U | I Leend

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d) State the conclusion in context. (Be sure to state it in terms of the problem) f . ¢ entudha awi dente ﬂnmr Hore 15 ’!. A a. H’ I e () ooN N ’[ méan nNUN bea | ( [ Hor H 4 !’,\j/k [._‘{,7 ¥ (o ¢) Based on your conclusion in part (c), what type of error might you be making and how do you reduce the probability of making that error 2 : Y Arnpcance Bl _I envys JMV\ L‘:’ )B(x{krf e (/ L‘j ffi,)é{( reasl W‘) tl’r‘i g ) i [\ e 'i\,k.l |\" 11. To test Ho: pt = 50 vs Hy: pu < 50 using sample data with ¥ = 43.7: ‘ (-/' a) Where will the randomization distribution be centered? | #e [ue £ e M = i ) < r ) y vAAUL - o Kan by fisn dghbvhon s Cerdered astn ; k\, o e i3 5 b) I§ this a left-tail test, a right-tail test, ora two-tail test? s s \[c(f"fm( (esC The nutrition label on a brand of iced tea says that the average amount of sugar per bottle is 25 grams. A chemical analysis of a sample of 30 bottles finds a mean of 33.8 grams of sugar per bottle. Test to see if this provides significant evidence that the true average is greater than 25. A randomization distribution for the test is shown, showing 1000 randomization statistics. [Show all details: state hypotheses, give notation and value of the sample statistic, use the randomization distribution to estimate the p-value, give a Sformal conclusion at a 5% level, and give a conclusion in context.| Ry M=258 H >05 m. M hence 20« 12. N\

cesssssvne sessescns 13. The Gallup Organization polled 1,024 U.S. adults about their opinions on gay/lesbiz.in relations and gay marriage. They found that 54% of those sampled viewed gay/lesbian relations as "morally acceptable" and that 50% felt that gay marriage should be legal. a) Define the appropriate parameter and state the hypotheses to test if this sample provides evidence that the proportion of American adults who support gay marriage differs from 50%. | \ oo M P = uv,w;‘;\‘ > ffir\t“r\'(fin :('UIB e SV;| 249 )j NRIN AT m Ho" T’;,—,Q g NS H':\',T)%D’g b) A 90% confidence interval for the proportion of American adults who support gay marriage is (0.475, 0.524). i Does this confidence interval provide evidence that the percentage of American adults who support gay marriage differs from 50%? If not, why? o L\f" HD Ce (( pnce WeNRI< Gre aabruged o male e eck [donCre jecdl e A s N A L » Ch of eudience. V. , ™ B (gl Yens OF c T o= l'm(‘] do ~SE have oAl 80 L e Shreryt il. State the significance level based on the confidence level used to construct the interval, o S 1:5,;‘&» - /fo = (b /" 14. Indicate whether it is best assessed by using a confidence interval or a hypothesis test or whether statistical inference is not relevant to answer it. i. On average, were the 23 players on the 2018 Canadian Olympic hockey team older than the 23 players on the 2018 US Olympic hockey team? Ars. & Hﬂ‘{.{\y/u[ wherence ¥ n& velesent

,[\ Coxy Ny’ mean 1§ ({.’.{,{, A t“ ted g'/‘“i’ ) 15 3 K ii. What is the average daily calorie intake of 20-year-old males? ;; »\!‘1""‘ 1,\1<,\4.t iii. Is there a significant difference in test scores between two groups? \‘\4 X \" 233 (¢ { \ ) If 15. A consumer protection agency is testing a sample of cans of tomato soup from a company. they find evidence that the average level of the chemical bisphenol A (BPA) in tomato soup from this company is less than 100 ppb (parts per billion), they will recall all the soup and sue the company. a). State the null and alternative hypotheses. f{\ v b). What does a Type I error mean in this situation.*! 1 1< fue ) 3 sallng alt f. seup nd sung e ‘““’“/”’j vy Dompanys Mme o pl@ :v]i‘c{e{J 1,en (L

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