Question

Question 13 of 14 (5 points) View problem in a pop-up 9.4 Section Exercise 18a,b,c,d,e The percentages of on-time arrivals for major U.S. airlines range from 68.6 to 91.1. Two regional airlines were surveyed with the following results. Ata = 0.05, is there a difference in proportions? Airline A Number of flights Number of on-time flights Airline B 312 241 Use P, for the proportion of on-time arrivals for airline A.
Find the critical values in ascending order and round the answer to two decimal places

Answer 1

necessary calculations:-

ni = 233, p = 165 233 = 0.7082

$n_{2}=312,\hat{p_{2}}=\frac{241}{312}=0.7724$

$\hat{p}=\frac{165+241}{233+312}=0.745$

hypothesis:-

$H_{0}:p_{1}-p_{2}=0$

H1 : p1 - P2 +0

test statistic be:-

$z=\frac{\hat{p_{1}}-\hat{p_{2}}}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}=\frac{0.7082-0.7724}{0.745(1-0.745*(\frac{1}{233}+\frac{1}{312})}=-1.70$

**THE PART YOU NEEDED**

z critical value for alpha= 0.05, both tailed test , both tailed test be:-

Zcrit = -1.96, 1.96

decision:-

$\left | z \right |=1.70<\left | z_{calc} \right |=1.96$

so, we fail to reject the null hypothesis and conclude that there is not sufficient evidence to claim that  there a difference in proportions

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