A survey was undertaken by Bruskin/Goldring Research for Quicken to determine ho

Question

A survey was undertaken by Bruskin/Goldring Research for Quicken to determine how people plan to meet their financial goals in the next year. Respondents were allowed to select more than one way to meet their goals. Thirty-one percent said that they were using a financial planner to help them meet their goals. Twenty-four percent were using family/friends to help them meet their financial goals, followed by broker/accountant (19%), computer software (17%), and books (14%) Suppose another researcher takes a similar survey of 675 people to test these results. Appendix A Statistical Tables (Round the intermediate values to 3 decimal places. Round your answer to 2 decimal places.) If 225 people respond that they are going to use a financial planner to help them meet their goals is this proportion enough evidence to reject the 31% figure generated in the Bruskin/Goldring survey using a = .10? The value of the test statistic is ______ and we ______. There enough evidence to declare that the proportion _______ than .31. If 175 respond that they are going to use family/friends to help them meet their financial goals is this result enough evidence to declare that the proportion is significantly higher than Bruskin/Goldring's figure of .24 if a = .05? The value of the test statistic is ______ and we _________. There _______ enough evidence to declare that the proportion ________ than .24. Eighteen percent of U.S.-based multinational companies provide an allowance for personal long-distance calls for executives living overseas, according to the Institute for International Human Resources and the National Foreign Trade Council Suppose a researcher thinks that U.S-based multinational companies are having a more difficult time recruiting executives to live overseas and that an increasing number of these companies are providing an allowance for personal long-distance calls to these executives to ease the burden of living away from home. To test this hypothesis, a new study is conducted by contacting 376 multinational companies. Twenty-two percent of these surveyed companies are providing an allowance for personal long-distance calls to executives living overseas. Does the test show enough evidence to declare that a significantly higher proportion of multinational companies provide a long-distance call allowance? Let a = .01. Appendix A Statistical Tables (Round your answer to 2 decimal places.) The value of the test statistic is z = ________ and we _______.

Explanation / Answer

Solution:

a) H0 : p = 0.31
Ha : p 0.31
n = 675 x = 225 1 = 0.10 2 = 0.05
Z0.005 = +1.645
p = x/n = 225/675 = 0.3333
z = p-p/sqrt[p-q/n]
= 0.3333-0.31/sqrt[(0.31)(0.69)/675]
= 1.31
Since the observed z = 1.31 is less than Z0.005 = 1.645, The decision is to fail to reject the null hypothesis. There is not enough evidence to declare that the proportion is any different than 0.31.

b) H0: p =0.24
Ha: p > 0.24
n = 675 x = 175 1 = 0.05 Z0.05 = 1.645
p = x/n = 175/675 = 0.2592
z = p-p/sqrt[p-q/n]
= 0.2592-0.24/sqrt[(0.24)(0.76)/675]
= 1.17
Since the observed z = 1.17 is less than Z0.005 = 1.645, The decision is to fail to reject the null hypothesis. There is not enough evidence to declare that the proportion is any different than 0.17.

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