STA2023 STATISTICs s 11:00 AM 1:45 PM STEVE ROIG-wATNIK 5E557 Quiz: Quiz #26: Se
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STA2023 STATISTICs s 11:00 AM 1:45 PM STEVE ROIG-wATNIK 5E557 Quiz: Quiz #26: Section 8.4 [Unit 4] 4/28/17 recommended Time Remaining This Question: 1 pt 1 of 10 (0 complete v This Quiz: 10 pts possible Question Help Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, critical value(s), and state the final conclusion that addresses the original claim. simple random sample of pages from a dictionary is obtained. Listed below are the numbers of words defined on those pages. Given that this dictionary has 1459 pages with defined words, the claim that there are more than 70,000 defined words is the same as the claim that the mean number of words on a page is greater than 48.0. Use a 0.10 level significance level to test this claim. What does the result suggest about the that there are more than 70.000 defined in the dictionary? 78 49 60 56 46 61 47 44 121 78 E click the icon to view a table of critical t-values What are the null and alternative hypotheses? O B. Ho: 48.0 O A. Ho u 48.0 1 u 48.0 H1: H 48.0 O D. Ho: 48.0 C. Ho H 48.0 H1 48.0 H1: 48.0 Identify the test statistic L (Round to three decimal places as needed) Click to select your answer(s) 50min Quiz w27 Sections 9 3.9 4 lunit 4]. 5/5/17 recommended deadline 05/06/17Explanation / Answer
Here the hypothesis is
H0 : mu = 48
H1 = mu > 48 , as the claim is that the mean is greater than 48 words on a page , so correct answer is d
the t stat is given as
t = x-mu /(s/sqrt(n))
we calculate x = 64 , and s = 23.49
t = (64 - 48)/(23.49/sqrt(10)) = 2.1539 , this is our t stat
the t critical value for df = 10-1 = 9 and alpha = 0.05 is 1.833 , from the t table. Please note that this is a 1 tail test as we are interested in the "GREATER than 48 "part of the test .
as our t stat (2.153) > t critical (1.833) , hence we reject the null hypothesis in favor of alernate hypothesis and conclude that Mu > 48 . hence there is sufficient evidence to conclude that there are more than 70000 words in a dictionary
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