Question

A survey asks 2000 workers. Has the economy forced you to reduce the amount of vacation you plan to its year Fry we percent of the surveyed say they are reducing the amount of vacation. Thirty workers participating in the survey are randomly selected. The random variable represente number of workers who werdengine amount of vacation. Decide where it is a binomialsperiment it is, de a success, specify the values of pandandi the possible values of the random varex is the experimenta binomial experiment? Yes O No What is a success in this experiment? Selecting a worker who is not reducing the amount of vacation Selecting a worker who is reducing the amount of vacation This is not a binomial experiment Specify the value of n. Select the correct choice below and in any answer boxes in your choice OB. This is not a binomial experiment Specify the value of p. Select the corect choice below and it in any answer boxes in your choice OAD- Type an integer or a decimal) OB. This is not a binomial experiment Specify the value of Select the correct choice below and in any answer boxes in your choice OA - (Type an integer or a decimal) your

Answer 1

1) Yes
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Selecting a worker who is reducing the amount of vacation
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A. n = 30
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A. p = 0.52
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A. q = 0.48

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2)

Total 142 187 329 2 Solution: The following cross tablulation have been provided. The row and column total have been calculated and they are shown below: Reading Math Science Urban 50 50 42 Suburban 70 63 54 Total 120 113 96 The expected values are computed in terms of row and column totals. In fact, the formula is E;; = R XC, where R; corresponds to the total sum of elements in rowi, C; corresponds to the total sum of elements in column , and T is the grand total. The table below shows the calculations to obtain the table with expected values: Expected Values Reading Math Science Urban 120x142 = 51.793 113x142 = 48.772 96x142 = 41.435 329 Suburban 120 x 187 = 68.207 113x187 = 64.228 329 329 Total 120 113 96 Based on the observed and expected values, the squared distances can be computed according to the following formula: (E-0) E. The table with squared distances is shown below: Squared Distances Reading Math Science (50-51.793) (42-41.435) Urban 51.703 41.485 0.062 0.031 0.008 Total 142 96x 187 = 54.565 187 329 = Suburban (70-68.207) 68 207 = 0.047 (63-64.228) 640 = 0.023 (54-54.565) 54565 0.006 Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: The two variables are independent H: The two variables are dependent This corresponds to a Chi-Square test of independence. Rejection Region Based on the information provided, the significance level is a = 0.01, the number of degrees of freedom is df = (2-1) (3-1) = 2, so then the rejection region for this test is R= {x?:X? > 9.21}.

Test Statistics The Chi-Squared statistic is computed as follows: x = (O; - E;) Ej 0.062 +0.047 +0.031 +0.023+0.008 +0.006 = 0.177 i=1 Decision about the null hypothesis Since it is observed that x? = 0.177 < x = 9.21, it is then concluded that the null hypothesis is not rejected Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is NOT enough evidence to claim that the two variables are dependent, at the 0.01 significance level. The corresponding p-value for the test is p = Pr(xi > 0.177) = 0.9152