Question

A recent National Science Foundation (NSF) survey indicates that more than 20% of the staff in American research and development laboratories is foreign. Results of the study have been used for pushing legislation aimed at controlling the number of foreign workers in the United States. An organization of foreign-born scientists wants to prove that the NSF survey results do not reflect the true percentage of foreign workers in the U.S. labs. The organization collects a sample of 5,000 laboratory workers in all major labs in the country and finds that 876 are foreign.

a). At 5% level of significance, is there sufficient evidence to conclude that the NSF study overestimated the percentage of foreigners in American laboratories? Your conclusion must be in terms of the P-Value as well as setting up a Rejection Region. Show work.

b). Which statistical distribution should be applied in this situation and why? Explain carefully.

c). What type of error is possible and describe this error in terms of the problem.

d). Based on a 95% confidence level, what is the best case and worst case scenario regarding the percentage of foreigners in American laboratories?

e). Carefully interpret this interval estimation.

f). Using the results of part (d), explain carefully whether or not there is sufficient evidence to conclude that the NSF study overestimated the percentage of foreigners in American laboratories? Explain carefully.

Answer 1

a). At 5% level of significance, is there sufficient evidence to conclude that the NSF study overestimated the percentage of foreigners in American laboratories? Your conclusion must be in terms of the P-Value as well as setting up a Rejection Region. Show work

b). Which statistical distribution should be applied in this situation and why? Explain carefully.
In this case, a person can be a foreigner or not.
Hence it is a normal distribution. But the sample size or n is very large we can approximate it to a normal distribution.

d). Based on a 95% confidence level, what are the best case and worst case scenario regarding the percentage of foreigners in American laboratories?

Best case scenario is 18.58% and the worst-case scenario is 16.46%.

e). Carefully interpret this interval estimation.
We are 95% confidence that the true proportion of the foreigners lie between the above-given interval.

f). Using the results of part (d), explain carefully whether or not there is sufficient evidence to conclude that the NSF study overestimated the percentage of foreigners in American laboratories? Explain carefully.

There is sufficient evidence to conclude that the NSF study overestimated the percentage of foreigners in American laboratories. We see that the 95% confidence interval indicate that 16.46% to 18.58% are foreigners which is not more than 20%.