1. According to a magazine article, 75% of all new jobs are at small businesses.

Question

1. According to a magazine article, 75% of all new jobs are at small businesses. In a random sample of 83 new jobs, 51 were at small businesses.  

A. If the population proportion is 75%, what is the probability of taking a random sample of n=83 and finding a sample proportion more extreme than the one observed in this sample? Use StatKey to determine this probability. Include a screenshot.

B. Given your results from part C, do you think that the proportion of all new small business jobs is less than 75%? Explain your reasoning.

Explanation / Answer

p^ = X/n = 51/83

Z =(p^ -p)/sqrt(pq/n)

Z = (p^ - 0.75)/sqrt(0.75*0.25/83)

P(p^ < 51/83)

P(Z < (51/83-- 0.75)/sqrt(0.75*0.25/83))

=P(Z < -2.8517)

=.002199

B) since 0.002199 < 0.05

we can conclude that that the proportion of all new small business jobs is less than 75%

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