Please help me answer this two questions QUESTION 1 QUESTION 2 13.2.17-T Questio

Question

Please help me answer this two questions

QUESTION 1

QUESTION 2

13.2.17-T Question Help The billing department of a national cable service company is conducting a study of how customers pay their monthly cable bills. The cable company accepts payment in person at a local office, by mail, by credit card, or by electronic funds transfer from a bank account. The cable company randomly sampled 400 customers to determine if there is a relationship between the customer's age and the payment method used. The accompanying sample results were obtained. Based on the sample data, can the cable company conclude that there is a relationship between the age of the customer and the payment method used? Conduct the appropriate test at the = 0.01 level of significance Click the icon to view the sample data. Chi-square goodness of fit test Chi-square test of independence One-way analysis of variance Two sample t-test Determine the null and alternative hypotheses. Choose the correct answer below. 0 A. Ho: The mean customer age is equal to the mean payment method. O B. Ho: The mean age for each payment method is equal O C. Ho: Customer's age is normally distributed. HA: The mean customer age is not equal to the mean payment method HA At least one mean for a payment method is not equal to the others. HA Customer's age is not normally distributed HA Customer's age is not independent of payment method. D. Ho: Customer's age is independent of payment method. Calculate the test statistic. The test statistic is (Round to two decimal places as needed.)

Explanation / Answer

Q1.

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 X and Y OR X and Y are independent

alternative, H1: exists a relation b/w X and Y OR X and Y are dependent

level of significance, = 0.01

from standard normal table, chi square value at right tailed, ^2 /2 =21.666

since our test is right tailed,reject Ho when ^2 o > 21.666

we use test statistic ^2 o = (Oi-Ei)^2/Ei

from the table , ^2 o = 54.251

critical value

the value of |^2 | at los 0.01 with d.f (r-1)(c-1)= ( 4 -1 ) * ( 4 - 1 ) = 3 * 3 = 9 is 21.666

we got | ^2| =54.251 & | ^2 | =21.666

make decision

hence value of | ^2 o | > | ^2 | and here we reject Ho

^2 p_value =0

ANSWERS

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null, Ho: no relation b/w X and Y OR X and Y are independent

alternative, H1: exists a relation b/w X and Y OR X and Y are dependent

test statistic: 54.251

critical value: 21.666

p-value:0

decision: reject Ho , there is suffcient evidence to conclude that one mean is not equal

Yes, the cable company can condude that there is a relationship between the age of the customer and the payment method used since H0 Is roected

MATRIX col1 col2 col3 TOTALS TOTALS row 2 8 11 10 12 41 row 3 29 66 71 59 225 row 3 25 19 4 7 55 row 4 22 35 17 5 79 TOTALS 84 131 102 83 400

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