Question

The Metal una county commissioners claim that a higher percentage o women work there than in 730 women in each county and find that neighboring Tungulu County. To test this, they randomly select 70sing in Metaluna, 502 women work and in Tungulu, 517 did not won you think the Miami County commissi distributed and samples are random. 0.1 level df work. Using a 0.1 level of significance, do oners are correct? Assuming that the populations are normally

Answer 1

N_m = 730, X_m = 502 Therefore estimated proportion, p_m = 502/730 = 0.688 n_t = 730, X_T = 730 - 517 = 213 Therefore estimated proportion, p_T = 213/730 = 0.292 *Null hypothesis, H_0: p_m = p_T Alternative hypothesis, H_a: p_m > p_T *Test statistic, z = p_m - p_T/squareroot p_m (1 - p_m)/n_m + p_T (1 - p_T)/n_T = 0.688 - 0.292/0.688 (1 - 0.688)/730 + 0.292 (1 - 0.292)/730 = 16.482 *significance level, alpha = 0.1 Therefore critical value, z_alpha = 1.282 *since our test statistics exceeds the critical value, we reject the null hypothesis, H_0 and conclude that higher percentage of women work in the metaluna than in neighboring Tungulu.