Chapter 9: Hypothesis Tests for a Single Population Mean Jonathan Hill Test the claim that the mean GPA of night students is larger than 3.1 at the 0.05 significance level. The null and alternative hypotheses would be: Question 1 0/1 pt 5 3 99 Ho:u = 3.1 Ho:p =0.775 Ho:/ = 3.1 Ho:u = 3.1 Ho:p = 0.775 Ho :p = 0.775 Statistics students believe that the mean score on a first statistics test is 65. The instructor thinks that H1:u> 3.1 H1: > 0.775 H1:u # 3.1 H1 :p 65 The significance level is: (to 2 decimals) B. State the mean of the sample: Based on this we: O Reject the null hypothesis C. State the standard error of the sample means: O Fail to reject the null hypothesis D. State the test statistic: t = Question Help: Message instructor E. State the p-value: . Question 3 0/1 pt 9 3 99 F. Decision: Reject the null hypothesis. O Fail to reject the null hypothesis. G. Hopefully you drew a picture of all of this. Question Help: Message instructor Question 2 0/1 pt 5 3 99Test the claim that the mean GPA of night students is significantly different than 2.5 at the 0.2 significance level. The null and alternative hypothesis would be: How. m 2.5 H01}; \".0625 Hazy. 2.5 Hazp _ 0.625 Hazp m 0.625 Hazy. = 2.5 H141. % 2.5 [11:12 #0625 H1:p. > 2.5 H1512 0.625 H1:/J. a Yy . Question 11 E' 0/1 Pt .0 3 H 99 b. The null and alternative hypotheses would be: Hg! '2 V Selectananswer V H1: '2 V Selectananswer V c. The test statistic 7 V = (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is '2 V or f. Based on this, we should Select an answer V the null hypothesis. g, Thus, the final conclusion is that The data suggest the populaton mean is significantly different from 15 at a = 0.10, so there is sufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is dilferent from 15. The data suggest that the population mean number of paintings that are in teachers houses is not significantly different from 15 at a = 0.10, so there is insufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is different from 15. The data suggest the population mean is not significantly different from 15 at or = 0.10, so there is sufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is equal to 15. h. lnterpret the p-vaiue in the context of the study. There is a 3.82% chance of a Type I error. If the population mean number of paintings that are in teachers' houses is 15 and it you survey another 15 teachers then there would be a 3.82% chance that the population mean would either be less than 14 or greater than 16. II the population mean number of paintings that are in teachers' houses is 15 and it you survey another 15 teachers, then there would be a 3.82% chance that the sample mean for these 15 teachers would either be less than 14 or greater than 16. There is a 3.82% chance that the population mean number of paintings that are in teachers' houses is not equal to 15. i. lnterpret the level of significance in the context of the study. II the population mean number of paintings that are in teachers' houses is 15 and it you survey another 15 teachers, then there would be a 10% chance that we would end up falsely concuding that the population mean number of paintings that are in teachers' houses is different from 15. It the population mean number of paintings that are in teachers' houses is different from 15 and if you survey another 15 teachers, then there would be a 10% chance that we would end up falsely concuding that the population mean number of paintings that are in teachers houses is equal to 15 According to the Carnegie unit system, the recommended number of hours students should study per ' unit is 2. Are statistics students' study hours more than the recommended number of hours per unit? There is a 10% chance that the population mean number af paintings that are in teachers' The data show the results of a survey of 13 statistics students who were asked how many hours per unit houses is different from 15. they studied. Assume a normal distribution for the population. There is a 10% chance that teachers are so poor that they are ali homeiess. 2.3. 0,5. 1.1, 1.4V 3.5, 2,2, 0.7, 1,7, 3, 2.9, 3.1, 0.9, 1.8 What can be concluded at the a = 0.10 level of significance? Hint: Helpful Videos: Calculations [*1 Setup [*1 Interpretations [*1 a. For this study, we should use Select an answer V HElP b. The null and alternative hypotheses would be: Ho: 7 v Select an answer V Question Help: E Message instructor :> H1: 7 V Select an answer V . Question 12 30/1 pt '03 .499 c. The test statistic ? V = (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places} e. The p-valueis ? V a f. Based on this, we should Selectan answer V the null hypothesis. g. Thus, the final conclusion is that The data suggest the populaton mean is significantly more than 2 at a = 0.10, so there is sufficient evidence to conclude that the population mean study time per unit for statistics students is more than 2. The data suggest the population mean is not significantly more than 2 at a = 0.10, so there is sufficient evidence to conclude that the population mean study time per unit for statistics students is equal to Z. The data suggest that the population mean study time per unit for statistics students is not significantly more than 2 at a = 0.10, so there is insufficient evidence to conclude that the population mean study time per unit for statistics students is more than 2. h. interpret the pvalue in the context of the study. There is a 30% chance that the population mean study time per unit for statistics students is greater than 2. There is a 50% chance of a Type I error. If the population mean study time per unit for statistics students is 2 and if you survey another 13 statistics students then there would be a 50% chance that the population mean study time per unit for statistics students would be greater than 2. If the population mean study time per unit for statistics students is 2 and if you survey another 13 statistics students then there would be a 50% chance that the sample mean for these 13 statistics students would be greater than 2. it interpret the 1evel of significance in the context of the study. If the population mean study time per unit for statistics students is 2 and if you survey another 13 statistics students, then there would be a 10% chance that we would end up falsely concuding that the population mean study time per unit for statistics students is more than 2. If the population mean study time per unit for statistics students is more than 7. and it you survey another 13 statistics students, then there would be a 10% chance that we would end up falsely concuding that the population mean study time per unit for statistics students is equal tn 2' There is a 10% chance that students just don't study at all so there is no point to this survey' There is a 10% chance that the pcpulation mean study time per unit fur statistics students is more than 2. Hint: Helpful Videos: Calculations [+] Setup [+] Interpretations [+] Help Question Help: 8 Message instructor