Question

please show all calculations! (feel free to use excel to help solve)

Brexit concerns may have affected trade flows, with cross-border shipments frequently delayed 35% of the time. Reports of a new Brexit deal might affect these delays. A random sample of 81 deliveries since the announcement reveals that 17 deliveries were late. Using a 5% level of significance, a test of whether the new Brexit deal affected the proportion of late deliveries leads to a calculated value of -0.824 with a pvalue of 0.044 and we reject the null in this two tailed test leads to a calculated value of -8.124 with a pvalue of 0.444 and we reject the null in this two tailed test leads to a calculated value of -0.198 with a pvalue of 0.004 and we reject the null in this upper tailed test leads to a calculated value of-2.64 with a pvalue of 0.004 and we reject the null in this two tailed test eads to a calculated value of-3.124 with a pvalue of 1.23 and we reject the null in this lower tailed test →

Answer 1

Let p be there proportion of late deliveries which affected by tnew Brexit deal.

In a random sample of 81 deliveries the new announcement reveals that 17 deliveries are late.

The sample proportion is

$\hat{p}=\frac{17}{81}$

$\hat{p}=0.2099$

At 5% level of significance we want to test the claim that the new Brexit deal affected the proportion of late deliveries.

The hypothesis testing problem is

$H_0:p=0.35$ vs $H_1:p \neq 0.35$

The test statistic is

$Z=\frac{\hat{p}-p}{\sqrt{\frac{p*(1-p)}{n}}}$

$Z=\frac{0.2099-0.35}{\sqrt{\frac{0.35*(1-0.35)}{81}}}$

$Z=\frac{-0.1401}{\sqrt{\frac{0.35*0.65}{81}}}$

$Z=\frac{-0.1401}{\sqrt{0.0028}}$

$Z=\frac{-0.1401}{0.0529}$

$Z=-2.648$

ie

$Z=-2.64$

The p value for the two tail test is

$p=2P(Z\leq-2.64)$​​​​​

$p=2*0.0041$ ##by using z table

$p=0.0082$

Since p value is less than 0.05, we reject the null hypothesis at 5% level of significance.

Therefore correct choice is 3.