Question

Literacy Refer to Exercise 2.

a. Find the probability that the proportion of graduates who pass the test is at most $0.20$higher than the proportion of dropouts who pass, assuming that the researcher’s report is correct.

b. Suppose that the difference (Graduate – Dropout) in the sample proportions who pass the test is exactly $0.20$. Based on your result in part (a), would this give you reason to doubt the researcher’s claim? Explain your reasoning.

Short answer

a. $\mathrm{P}(z<-2.61)=0.00453$

b. Due to small value of probability, there is reason to doubt company's claim.

Step-by-step solution

Given Information

It is given that $\mu =0.40$

$\sigma =0.07745$

${\hat{p}}_G-{\hat{p}}_D=0.20$

Calculation of Probability

Using $z=\frac{x-\mu }{\sigma }$

$=\frac{0.20-0.40}{0.07745}\approx -2.61$

Hence, $\mathrm{P}(z<-2.61)=0.00453$

$=0.45\%$

Reason to Doubt Company's Claim

As we have calculated $\mathrm{P}(z<-2.61)=0.00453$. Is is very small.

There is reason to doubt company's claim.