A recent National Science Foundation (NSF) survey indicates thatmore than 20% of the staff in American research and developmentlaboratories is foreign. Results of the study have been used forpushing legislation aimed at controlling the number of foreignworkers in the United States. An organization of foreign-bornscientists wants to prove that the NSF survey results do notreflect the true percentage of foreign workers in the U.S. labs.The organization collects a sample of 5,000 laboratory workers inall major labs in the country and finds that 876 are foreign.
a). At 5% level of significance, is there sufficient evidence toconclude that the NSF study overestimated the percentage offoreigners in American laboratories? Your conclusion must be interms of the P-Value as well as setting up a Rejection Region. Showwork.
b). Which statistical distribution should be applied in thissituation and why? Explain carefully.
c). What type of error is possible and describe this error interms of the problem.
d). Based on a 95% confidence level, what is the best case andworst case scenario regarding the percentage of foreigners inAmerican laboratories?
e). Carefully interpret this interval estimation.
f). Using the results of part (d), explain carefully whether ornot there is sufficient evidence to conclude that the NSF studyoverestimated the percentage of foreigners in Americanlaboratories? Explain carefully.
