Question

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? The data show the results of a survey of 13 statistics students who were asked how many hours per unit they studied. Assume a normal distribution for the population. 3.1, 2.6, 2.9, 4.2, 3.9, 1.9, 0.6, 2.4, 0.8, 2.7, 4.3, 3.7, 2.1 What can be concluded at the α α = 0.05 level of significance? a.For this study, we should use Select an answer z-test for a population proportion t-test for a population mean b.The null and alternative hypotheses would be: H0: H0: ? p μ ? ≠ < = > H1: H1: ? μ p ? ≠ > < = c.The test statistic ? t z = (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 ? ≤ > α α f.Based on this, we should Select an answer fail to reject reject accept the null hypothesis. g.Thus, the final conclusion is that ... The data suggest the population mean is not significantly more than 2 at α α = 0.05, so there is sufficient evidence to conclude that the population mean study time per unit for statistics students is equal to 2. The data suggest that the population mean study time per unit for statistics students is not significantly more than 2 at α α = 0.05, so there is insufficient evidence to conclude that the population mean study time per unit for statistics students is more than 2. The data suggest the populaton mean is significantly more than 2 at α α = 0.05, so there is sufficient evidence to conclude that the population mean study time per unit for statistics students is more than 2. h.Interpret the p-value in the context of the study. There is a 2.53303373% chance that the population mean study time per unit for statistics students is greater than 2. There is a 2.53303373% 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 2.53303373% 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 2.53303373% chance that the sample mean for these 13 statistics students would be greater than 2.71. i.Interpret the level of significance in the context of the study. There is a 5% chance that the population mean study time per unit for statistics students is more than 2. There is a 5% chance that students just don't study at all so there is no point to this survey. 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 5% 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 2 and if you survey another 13 statistics students, then there would be a 5% chance that we would end up falsely concuding that the population mean study time per unit for statistics students is equal to 2.

Answer 1

g) Thus, the final conclusion is that -

The data suggest the population mean is significantly more than 2 at α α = 0.05, so there is sufficient evidence to conclude that the population mean study time per unit for statistics students is more than 2.

h) 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 2.53303373% chance that the sample mean for these 13 statistics students would be greater than 2.71.

i) There is a 5% chance that students just don't study at all so there is no point to this survey. 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 5% chance that we would end up falsely concuding that the population mean study time per unit for statistics students is more than 2.