QUESTION 4 (a) The directot of a daily newpapert is desinious of investigating t

Question

QUESTION 4 (a) The directot of a daily newpapert is desinious of investigating the relationship between the a reads first. One thousand, reader's area of residence and the section of the paper he or she one hundred and sixty-five readers of the newspaper were surveyed. The data gathered was in a contingency table. See Table 2 below Table 2 Section of newspaper read first Newr SportsEntertainment Area of Lzad Total residence Raral Urban Total Stories 150 167 317 119 122 241 102 98 200 115 100 215 100 92 192 586 579 1165 The director asked you to assist with conducting an appropriate hypothesis test to detemine whether there is a relationship between the type of community the reader's area of residence and the section of the paper he or she reads first. 0. State the type of hypothesis test that is appropriate for this investigation. I mark] (n). Catefully state the null and alternative hypotheses of this test. (in). Determine the degrees of freedom for this test. [2 marks] 2 marks) The information in Table 2 above was inputted in MINITAB for further analysis. MINITAB gencrated the resulrs shown in Exhibit 2 below Exhibit 2 Chi-square -2.367, DF (purposely deleted), P-value 0.6686 rv). Assist the director to make a conclusion for this test? Give reasons for your answer. 5 marks) (b) The manufacturers of a certain brand of laptops claim that the mean lifespan of their laptops is 6 years. A disgruntled customer believes that the manufacturers are overstating the lifespan of these laptops, while another customer is satisfied with the claim. A researcher randomly selected 80 individuals who previously owned this brand of laptop and found that the sample mean lifespan was 5.8 years with a standard deviation of 1.1 years. Assuming that the population is normally distributed, test, at the 5% level of significance, whether the manufacturers are incorrectly estimating the mean lifespan of the laptops, by answering the [10 marks following Total 20 marks © The Univentry of Trinidad & Tobago December 2016 Final Examinations MATH2005 Prob and Stats i Page 6 of 9

Explanation / Answer

Given table data is as below

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calculation formula for E table matrix

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expected frequecies calculated by applying E - table matrix formulae

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calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above

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set up null vs alternative as
null, Ho: no relation b/w type of community and section of the paper
alternative, H1: exists a relation b/w type of community and section of the paper
level of significance, = 0.05
from standard normal table, chi square value at right tailed, ^2 /2 =9.4877
since our test is right tailed,reject Ho when ^2 o > 9.4877
we use test statistic ^2 o = (Oi-Ei)^2/Ei
from the table , ^2 o = 2.3669
critical value
the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 5 - 1 ) = 1 * 4 = 4 is 9.4877
we got | ^2| =2.3669 & | ^2 | =9.4877
make decision
hence value of | ^2 o | < | ^2 | and here we do not reject Ho
^2 p_value =0.6686
ANSWERS
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null, Ho: no relation b/w type of community and section of the paper
alternative, H1: exists a relation b/w type of community and section of the paper

test statistic: 2.367

critical value: 9.4877

p-value:0.6686

decision: do not reject Ho

degrees of freedom = 4

not exists a relation b/w type of community and section of the paper

MATRIX col1 col2 col3 col4 col5 TOTALS row 1 150 119 102 115 100 586 row 2 167 122 98 100 92 579 TOTALS 317 241 200 215 192 N = 1165

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