modern business 1. Speaking to a group of analysts in January 2006, a brokerage
ID: 3335634 • Letter: M
Question
modern business 1. Speaking to a group of analysts in January 2006, a brokerage firm executive claimed that at least 70% of investors are currently confident of meeting their investment objectives. A UBS Investor Optimism Survey, conducted over the period January 2 to January 15, found that 67% of investors were confident of meeting their investment objectives (CNBC, Jan- uary 20, 2006). a. Formulate the hypotheses that can be used to test the validity of the brokerage firm executive's claim. Assume the UBS Investor Optimism Survey collected information from 300 investors. What is the p-value for the hypothesis test? At = .05, should the executive's claim be rejected? b. C. Center for I ogistics Management, 6% of all menExplanation / Answer
Q.41
H0 : At least 70% of investors are currently cofident of meeting their investment objectives. p >= 0.70
Ha : Less than 70% of total investors are currently confident of meeting their investment obejectives. p < 0.70
(b) Number of investors = 300
proportion of investors who are confident of meeting their objectives p^ = 0.67
standard error of the proportion se0 = sqrt [p0 * (1-p0)/ N] = sqrt [0.70 * 0.30/300] = 0.02645
Test statistic
Z = (p^ - p0)/ se0 = (0.67 - 0.70)/ 0.02645 = -1.13
so P - value = Pr(Z < -1.13) = 0.1292 (as one sided test)
(C) so as p - value > 0.05 so we shall not reject the null hypothesis and can claim that At least 70% of investors are currently cofident of meeting their investment objectives.
Question 2
H0 : 75% of women wear shoes that are too small. p = 0.70
Ha : Proportion of women who wear shoes that are too small are different than 0.75. p 0.70
Number of women in sample = 400
proportion of investors who are confident of meeting their objectives p^ = 292/400 = 0.73
standard error of the proportion se0 = sqrt [p0 * (1-p0)/ N] = sqrt [0.73 * 0.27/400] = 0.0222
Test statistic
Z = (p^ - p0)/ se0 = (0.73 - 0.75)/ 0.0222 = -0.9
so P - value = 2 * Pr(Z < -0.9) = 2 * 0.1841 = 0.3682 (as two sided test)
so as p - value > 0.05 so we shall not reject the null hypothesis and can claim t75% of women wear shoes that are too small.
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