Question

According to the Carnegie unit system, the recommended number of hours students should study per unit is 2. Are statistics students' study hours less than the recommended number of hours per unit? The data show the results of a survey of 14 statistics students who were asked how many hours per unit they studied. Assume a normal distribution for the population.

0, 2.5, 0, 1.4, 2.7, 3.2, 0, 3.2, 2.5, 0.6, 1.7, 0, 3, 2.2

What can be concluded at the αα = 0.10 level of significance?

1. For this study, we should use Select an answer z-test for a population proportion t-test for a population mean
2. The null and alternative hypotheses would be:

H0:H0:  ? μ p  ? = > < ≠       

H1:H1:  ? μ p  ? = < ≠ >    

3. The test statistic ? z t  =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? ≤ >  αα
6. Based on this, we should Select an answer fail to reject reject accept  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest that the population mean study time per unit for statistics students is not significantly less than 2 at αα = 0.10, so there is insufficient evidence to conclude that the population mean study time per unit for statistics students is less than 2.
   • The data suggest the population mean is not significantly less than 2 at αα = 0.10, 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 the populaton mean is significantly less than 2 at αα = 0.10, so there is sufficient evidence to conclude that the population mean study time per unit for statistics students is less than 2.
8. Interpret the p-value in the context of the study.
   • There is a 15.90345232% chance that the population mean study time per unit for statistics students is less than 2.
   • There is a 15.90345232% chance of a Type I error.
   • If the population mean study time per unit for statistics students is 2 and if you survey another 14 statistics students, then there would be a 15.90345232% chance that the population mean study time per unit for statistics students would be less than 2.
   • If the population mean study time per unit for statistics students is 2 and if you survey another 14 statistics students, then there would be a 15.90345232% chance that the sample mean for these 14 statistics students would be less than 1.64.
9. Interpret the level of significance in the context of the study.
   • There is a 10% chance that the population mean study time per unit for statistics students is less than 2.
   • There is a 10% 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 14 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 less than 2.
   • If the population mean study time per unit for statistics students is less than 2 and if you survey another 14 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 to 2.

Answer 1

Answer:

According to the Carnegie unit system, the recommended number of hours students should study per unit is 2. Are statistics students' study hours less than the recommended number of hours per unit? The data show the results of a survey of 14 statistics students who were asked how many hours per unit they studied. Assume a normal distribution for the population.

0, 2.5, 0, 1.4, 2.7, 3.2, 0, 3.2, 2.5, 0.6, 1.7, 0, 3, 2.2

What can be concluded at the α = 0.10 level of significance?

1. For this study, we should use Select an answer t-test for a population mean
2. The null and alternative hypotheses would be:

H0: μ = 2.0      

H1:μ < 2.0  

3. The test statistic ? t  = -1.038  (please show your answer to 3 decimal places.)
4. The p-value = 0.1590 (Please show your answer to 4 decimal places.)
5. The p-value is >  α
6. Based on this, we should Select an answer fail to reject the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest that the population mean study time per unit for statistics students is not significantly less than 2 at αα = 0.10, so there is insufficient evidence to conclude that the population mean study time per unit for statistics students is less than 2.
8. Interpret the p-value in the context of the study.
   • If the population mean study time per unit for statistics students is 2 and if you survey another 14 statistics students, then there would be a 15.90345232% chance that the sample mean for these 14 statistics students would be less than 1.64.
1. Interpret the level 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 14 statistics students, then there would be a 10% chance that we would end up falsely concluding that the population mean study time per unit for statistics students is less than 2.

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	2
Level of Significance	0.1
Sample Size	14
Sample Mean	1.6429
Sample Standard Deviation	1.2870
Intermediate Calculations
Standard Error of the Mean	0.3440
Degrees of Freedom	13
t Test Statistic	-1.0383
Lower-Tail Test
Lower Critical Value	-1.3502
p-Value	0.1590
Do not reject the null hypothesis