A well-known brokerage firm executive claimed that at least 49 % of investors are currently confident of meeting their investment goals.

Question

An XYZ Investor Optimism Survey, conducted over a two week period, found that out of 84 randomly selected people, 43 of them said they are confident of meeting their goals. Suppose you are have the following null and alternative hypotheses for a test you are running:

Ho= u=49

Ha= u=/49

Calculate the test statistic, rounded to 3 decimal places

z=

how to solve with ti 84, by hand or any other way please.

Answer 1

Compute the Z test for a single proportion z = (p - p0)/std. dev. such that std. dev = (p (1-p)/n)**.5. In this case p = .49/84 = .5119, n = 84, p0=49. sd = .5454, Z = 0.4016. Accept the null hypothesis.