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Question

Tina Dennis is the comptroller for Meek Industries. She believes that the current cash-flow problem at Meek is due to the slow collection of accounts receivable. She believes that more than 60% of the accounts are in arrears more than 3 months. A random sample of 200 accounts showed that 140 were more than 3 months old. At the 0.01 significance level, can she conclude that more than 60% of the accounts are in arrears for more than three months?

1. Make the decision rule.

H0 is rejected if z > ____

1. Evaluate the test statistic

Test statistic ____

Answer 1

p=.6

q=.4

n=200

x=140

p-hat=140/200=.7

alpha= .01

np=120>=5

nq=80>=5

(therefore standard normal, z)

H₀: p<=.6

H_a:p>.6

z_crit=2.33 (from tables, area in tail is alpha)

z_test=(.7-.6)/sqrt(.6*.4/200) = 2.89

2.89 > 2.33 therefore in Rejection Region

Reject H₀. There is sufficient evidence to suggest that more than 60% of accounts are more than 30 days in arrears.