Manilias is a country with population spread out in seven regions. The regions Apolia, Boelia, Cuilia, Dealia, Euolia, Fiolia and Giolia, have 35%, 20%, 15%, 10%, 10%, 8% and 2% of the country population, respectively. In an attempt to study if the proportion of graduates among the working population is homogeneous across different regions in the country, a total of 200 working adults were sampled from seven regions. The number of adults sampled from each region is according to the relative population proportion in that region. The number of graduates in samples from Apolia, Boelia, Cuilia, Dealia, Euolia, Fiolia and Giolia are 18, 14, 11, 5, 8, a and b. a and b are unknown numbers as the results from the sampling were misplaced. But it is known that 30% of the total sampled are graduates. Carry out an appropriate chi-square hypothesis test. (a) State the null and alternative hypotheses. (b) Construct the contingency table with the observed frequencies, together with the marginal totals. (c) Calculate the expected frequencies under the null hypothesis, and clearly display the expected frequencies in the contingency table from part (b) above. (d) Describe what has to be done with the data to ensure the accuracy of the chi-square test. (e) Calculate the test statistic value. (f) Write down the critical value of the test and specify the rejection region. (g) Draw an appropriate conclusion from the test.
Manilias is a country with population spread out in seven regions. The regions Apolia, Boelia, Cuilia, Dealia, Euolia, Fiolia and Giolia, have 35%, 20%, 15%, 10%, 10%, 8% and 2% of the country population, respectively.
In an attempt to study if the proportion of graduates among the working population is homogeneous across different regions in the country, a total of 200 working adults were sampled from seven regions. The number of adults sampled from each region is according to the relative population proportion in that region.
The number of graduates in samples from Apolia, Boelia, Cuilia, Dealia, Euolia, Fiolia and Giolia are 18, 14, 11, 5, 8, a and b. a and b are unknown numbers as the results from the sampling were misplaced. But it is known that 30% of the total sampled are graduates.
Carry out an appropriate chi-square hypothesis test.
(a) State the null and alternative hypotheses.
(b) Construct the
(c) Calculate the expected frequencies under the null hypothesis, and clearly display the expected frequencies in the contingency table from part (b) above.
(d) Describe what has to be done with the data to ensure the accuracy of the chi-square test.
(e) Calculate the test statistic value.
(f) Write down the critical value of the test and specify the rejection region.
(g) Draw an appropriate conclusion from the test.
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