Z Test Hypothesis for Population Proportions

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 272 of 400 investors were confident of meeting their investment objectives (CNBC, January 20, 2006). Test the executive's claim against the suitable alternative at α = .05.

a) In proper notation, state the hypotheses of this test.

b) Show your calculation of the test statistic. ______ = ______________

c) Give the p-value of the test to 4 decimals. p = ________________________

d) What is the conclusion about the issue in question ?

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