Question

American consumers with credit scores below 600 have a very difficult time getting approved for loans. Last year 30% of Americans had a credit score below 600. Due to the recent financial crisis, the US Government is concerned that this proportion has increased. To analyze this, a simple random sample of 400 Americans was selected for this study, and 140 people had credit scores less than 600. Use α = 0.05.

a) State the null and alternative hypotheses in the context of the question.

b) Calculate the value of the test statistic. Check the required condition(s) to validate the test statistic.

c) Find the p-value.

d) What conclusion can we draw?

Answer 1

solution :- Since, npo snel-po) both exceeds 5 a Ho: p=0.30 Ha: pso.30 npo = 400 x 0.30 = 120 n 10-po) : 400X0.70 = 280 by and somple size is less than 10% of population size. call the conditions are saksfied Х Test statistic Р 140 -0.30 400 pll-p) 0.3 X 0.7 400 2.18 c) P-value = P(2*2.18) Plz) 2.18) = 1- P1262.13) - 0.0146 d) since, P- ralue <a | Reject Ho There is sufficient evidence to conclude that proportion of people had credit score less than 600 has increased.