In February 2008, the Gallup organization surveyed 1,034 adults between 30 and 64 years of age...

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In February 2008, the Gallup organization surveyed 1,034 adults between 30 and 64 years of age and found that 548 were worried that they will outlive their money after they retire. Does the sample evidence suggest that a majority of 30- to 64-year-olds in the United States are worried they will outlive their money? Use the a 0.05 level 2. of significance: (a) Regarding a population proportion, what condition must be provided? (b) Determine the alternative hypothesis if the null hypothesis is p (c) Show the critical value approach. (d) Show the P-value approach. 0.5. (e) Decide whether you reject the null hypothesis or not. Then state the conclusion.

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a) The condition is np 210 and n(1-p)210. Here np (1034) (0.5)-517 ann(1- p) 1034(0.5) 517 Condition satisfied

35 b) Null hypothesis,H0: Alternative hypothesis H1 p0.5 sample proportion: P Sample size: Standard error: p(1- p 0.01555 0.5 Here,x= 548 0.32998 n1034 72 Test statistic: = 1.93 p(1-p)

c)Level of significance: α- Critical value : a- 1.64 Critical region: z > -α 1.64 Reject the null hypothesis

For z= 1.93 The right tailed p-value is 0.0268 Decision: Since p-value 〈 α, we reject HO e) Re ject the null hypothesis Ho Conclusion: There is sufficient evidence to conclude that the majority of 30-64 year olds in the United States are worried

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