Question

the XYZ Association surveyed retired senior executives who had returned to work. They found that after returning to work, 38% were employed by another organization, 32% were self-employed, 23% were either freelancing or consulting, and 7% had formed their own companies. To see if these percentages are consistent with the of Bahrain residents, a local researcher surveyed 300 retired executives who had returned to work and found that 122 were working for another company, 85 were self-employed, 76 were either freelancing or consulting, and 17 had formed their own companies. At the 10% significance level, test the claim that the percentages are the same for those people in Bahrain.

Answer 1

Answer Date: 07/06/2020 To test the claim is that the percentages are not same as those people in Bahrain at 10% significance level. The null and alternative hypothesis is, The null hypothesis is that the percentages are the same for those people in Bahrain. The alternative hypothesis is that the percentages are not same as those people in Bahrain. The chi-square test statistic is, First, find frequency expected then compute chi-square test statistics. The expected frequency for employed by another organization is, fe = Npi = 300 x 38% =114

The expected frequency for self-employed is, fe = Npi = 300 x 32% = 96 The expected frequency for either freelancing or consulting is, fe= Npi = 300 x 23% = 69 The expected frequency for formed their own companies is, fe = Npi = 300 x 7% = 21 The chi-square test statistic is,

x = (fo-fr) fe (122 – 114)2 (85 – 96)2 (76–69)2 (17–21)? 114 96 69 21 = 3.294 + + The chi-square test statistic is 3.294 The chi-square critical value is, Compute degrees of freedom for finding chi-square critical values. d.f. = k-1 = 4-1 = 3 From the critical value table, show degrees of freedom 3 and the significance level 0.10, so the chi-square critical value is 6.251. The chi-square critical value is 6.251

Decision The conclusion is that chi-square test statistic 3.294 less than chi-square critical value 6.251, so the null hypothesis is not rejected at 10% level of significance. There is insufficient evidence to indicate that the percentages are not same as those people in Bahrain. The result is not statistically significant.