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Hypothesis Testing using the Rejection Region Method A coffee shop owner claims that her employees' average hourly salary & more than $18.10. You survey 31 employees and find they have an average hourly salary of $18.04 with a standard deviation of $2.60, test this claim at a 0.01 level of significance. a. ) The claim belongs to the O The null hypothesis Ho. The alternative hypothesis Ha. b.) Which represents the hypothesis statement? Ho: =18.10 Ho:p 2 18.10 M:A $ 18.10 Ha:p # 18.10 Ha:p 18.10 C. ) What is the direction of the tail? O right tail two tail O left tail d. ) Which test will be used? The 7-test because we are testing for a mean with the population standard deviation known. The t test because we are testing for a mean with the population standard deviation unknown. The Z-test because we are testing for a proportion. e.) Find the critical value used to create the rejection region. (exact table value) f.) Calculate the test statistic. 12 decimal places) E-) Is the test statistic in the rejection region? O Yes. We reject Io and support Hu. O No. We fail to reject Ho and fail to support H. . Conclusion Statement h.) Choose the correction conclusion statement. O At the 0.III level of signficance, there is enough evidence to support the owner's claim that his employees average hourly salary is more than $18.10. O At the 0.01 level of signficance, there is NOT enough evidence to support the owner's claim that his employees average hourly salary is more than $18.10. At the 0.01 level of signficance, there is enough evidence to reject the owners claim that his employees average hourly salary is more than $18.10, O At the 0.01 level of significance, there is NOT enough evidence to reject the owners claim that his employees average hourly salary is more than $14. 10.Hypothesis Testing using the p-value Method A local newspaper declares that 55 % of 18 year olds in our state possess a driver's license. You survey 77 residents who are 18 years old and find that 35 possess a driver's license. Test this claim at a 0.05 level of significance. a. ) The claim belongs to the The null hypothesis Ho- The alternative hypothesis Ha. b.) Which represents the hypothesis statement? Ho:p x 0.55 Ho: p =0.55 Ho:p 0.55 Ha :p > 0.55 H. :p / 0.55 H. :p -= 0.55 c. ) What is the direction of the tail? O two tail O right tail O left tail d. ] Which test will be used? The 7-test because we are testing for a mean with the population standard deviation known. The t test because we are testing for a mean with the population standard deviation known. O The Z-test because we are testing for a proportion. e.) The sample proportion p-hat is p # (use fraction) f.) Calculate the test statistic. (2 decimal places) 8.) The p-value is (4 decimal places) h.) Is the p-value less than c = 0.057 Yes. We reject Ho and support H.. No. We fail to reject Ho and fail to support Ha. Conclusion Statement i. ) Choose the correction conclusion statement. O At the 0.05 level of significance, there is NOT enough evidence to support the claim that 55 % of 18 year olds possess a driver's license. O At the 0.05 level of significance, there is enough evidence to reject the claim that 55 % of 18 year olds possess a driver's license. At the 0.05 level of significance, there is NOT enough evidence to reject the claim that 55 % or 18 year olds possess a driver's license. Q At the 0.05 level of significance, there is enough evidence to support the claim that 55 % of 189.5 Hypothesis Testing for Proportions Using the p-Value (Z-test) A well-known brokerage firm executive claimed that 30% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 800 people, 31% of them said they are confident of meeting their goals. Test the claim that the proportion of people who are confident is larger than 30% at the .01 significance level. a.) The null and alternative hypothesis would be: Ho:p 03 Ho :p 03 Hq:p > 0.3 H, : /4 = 0.3 Ha:p 03 H,:p 303 Hap