Σ known popul approx normal σ known use s to

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σ known ? Popul.  approx. normal  ? σ known ? Use  s to estimate  σ Use  s to estimate  σ Increase  n to > 30 / x z n μ σ - = / x z s n μ - = / x z n μ σ - = / x t s n μ - = Yes Yes Yes Yes No No No No 16
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17
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18 Tests about Population Proportion The null and alternative hypotheses are similar to the case of sample mean. Three cases: H 0 : p > p 0 H 0 : p < p 0 H 0 : p = p 0 H a : p < p 0 H a : p > p 0 H a : p p 0 where p 0 is the hypothesized value of proportion. Test about population proportion--Large Sample Case Check np 0 > 5 and n(1-p 0 ) > 5 Test statistic where Rejection Rule: One-Tailed Two-Tailed H 0 : p p 0 Reject H 0 if z > z α H 0 : p p 0 Reject H 0 if z < -z α H 0 : p  p 0 Reject H 0 if |z| > z α/2 18
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<Remark> Reject H 0 if p-value< α Example: Poll At least 20% of all workers are believed to be willing to work fewer hours for less pay to obtain more time for personal and leisure activities. A USA Today/CNN/Gallup poll with a sample of 596 respondents found 83 willing to work fewer hours for less pay to obtain more personal and leisure time. Use a .05 level of significance to determine whether the proportion of all workers willing to work fewer hours to obtain more personal time is less than 20%. 19
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20 Chapter 9: Practice Problems Q1. The manager of a travel agency is considering a new promotion plan in order to increase sales. Currently, the average sales rate per agent is 25 trips per month. The manager wants to determine whether the new promotion plan increases the average sales rate per agent. a. Develop the appropriate null and alternative hypotheses. b. What is the Type I error in this case? What is the consequence of making this error? c. What is the Type II error in this case? What is the consequence of making this error? 20
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Q2. According to the National Association of Colleges and Employers, the 2000 mean annual salary of business degree graduates in accounting was $37,000 ( Time , May 8, 2000). In a follow-up study in June 2001, a sample of 48 graduating accounting majors found a sample mean of $38,100 and a sample standard deviation of $5,200. Determine whether the mean annual salary of June 2001 graduates in accounting has increased compared to the 2000 mean annual salary. a. Formulate the appropriate null and alternative hypotheses. b. What is the value of the test statistic? c. Compute the p-value. d. Using what is the conclusion? (Use both critical value and the p-value) e. What is the conclusion at 10% level of significance? Q3. Evening long-distance phone calls of Purdue students usually average 20.3 minutes per call. Recently, in a random sample of 36 calls, the sample mean time is found to be 18.8 minutes per call, with a sample standard deviation of 6 minutes. 21
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22 Use this data to determine whether the mean duration of long-distance phone calls of Purdue students has changed recently. a. Write the appropriate null and alternative hypotheses.
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  • Spring '08
  • Priya
  • Statistics, Null hypothesis, Statistical hypothesis testing, Type I and type II errors, alternative hypotheses

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