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Stats Quiz 7B

# Stats Quiz 7B - le Stat 1719 Quiz 7B Name Red id l(2 point...

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Unformatted text preview: le Stat 1719 Quiz 7B Name: Red id: l. (2 point) Does taking a lab class improve students“ scores on a statistics ﬁnal? Exam scores for students not taking the lab class are normally distributed with mean ,u m 74 and standard deviationcs‘ m 10. Researchers assign 5,000 statistics students to take a lab class in addition to the regular statistics class. The mean score for these students is 74.} They test the hypotheses H0: ,u = 74 against H3: [.1 > 74 The pwalue for the test is less than 0.0001. Which of the following is true? A. The researcher has substantial evidence that the mean score for students taking the fix lab class has substantially improved. £32} There is strong evidence that scores improved, but the improvement was not substantial. C. The researcher has proved that the mean score for students taking the lab class has substantially improved. D. There is not evidence that scores improved when the students took the lab class concurrently with the statistics class. Answer: 2. The lifetime (in hours) of a certain type of light bulb is known to be normally distributed. 169 such bulbs were used to obtain a 98% confidence interval estimate of the true nieau lifetime of the light bulbs. The conﬁdence interval was calculated to be (1334.9, l365.l) The manufacturer of this type of light bulbs claims that they last. on average, 1350 hours. Test the claim, using the confidence intervalgiven. l. {2 points) ldentif the null and alternative hypotheses. ﬁaiﬁi? iﬁgﬁ decision. ihgﬁ ill. (1 point) What would the level of significance of the hypothesis test he? sis: Swag? ﬁsh‘s“ Use the following information to answer gaestions 34 Suppose that a random survey of 34 teenagers found that the average amount of time they spend on the Internet each day is 3.2 hours with a standard deviation of 0.78 hours. 3. (1. point) What assumption must be made in order for a conﬁdence interval to be valid? eraiaiagsm as {l s... g g“? 4. (3 points) Calculate a 90% confidence interval estimate for the average amount of time a a teenager spends on the Internet each day. “n3 dig % it as. : riiaaa‘itaaa‘} Bit mm. as; :§:;%?Q if siaase . same} if 5. (1 point) A certain population follows a normal distribution with unknown mean ,u and standard deviation 2.5. You collect data and test : HQ 1}}. m 5 vs. Ha : t: a 5 You obtain a P—vatne of 0.022. Which of the-following is true? 3 Q at; ﬁé a a”? gagﬂ A. A 90% conﬁdence interval for y Will inctude the value 5. at ﬁt i g ig} A 99% conﬁdence interval for y will inclade the value 5 ea; igi g? . ' a; g, 1 tag?“ % C. A 95% conﬁdence interval for ,u will include the value 5. aim a {mi 9% ' ' D. None of the conﬁdence intervals listed above will include the value 5 Answer 6. {6 points) A drug manufacmrer produces an antibiotic in large fermentation vats. To determine the average potency for the batch of antibiotic being prepared, the vat is sampled at ll different locations. The potency readings of the antibiotic are recorded 352W. follows: X :; gt 3% §% 8.7 9.0 9.} 8.8 8.8 9.0 8.4 9.2 9,0 8.7 9.1 W g QEQE If the potency of the antibiotic is stated to be 9.0, is there signiﬁcant evidence that the mean potency is less than the stated value? Assume the necessary conditions are met to conduct a hypothesis test. a. State the approprtate null and alternative hypotheses tit: c. Calculate the corresponding p-value. ﬁg a?“ sataa é. @333 d. Make a statistical decision using a level of signiﬁcance of 0.05. J ustify your decision. ﬁaatae F . ﬁg at; ewlnterpret your decision in the context f the problem ‘ eat s ‘ eaten“ at” 7. (3 points) To assess the accuracy of a laboratory scale, a standard weight known to weigh 10 grams is weighed repeatedly. The scale readings are normally distributed with an estimated standard deviation of 0.0002 gram How many measurements must be averaged to get a margin of error of 0.0001 with 95% conﬁdence? t3 W: inﬂame?“ 2..- seats 2... tag: Egg; {,nﬁe‘ﬁ a §§i§l a gt’t'af i _ a gs. 3 eat? ...
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