The average house has 10 paintings on its walls. Is the meansmaller for houses owned by teachers? The data show the results ofa survey of 14 teachers who were asked how many paintings they havein their houses. Assume that the distribution of the population isnormal.

7, 11, 8, 10, 10, 7, 7, 7, 11, 10, 7, 8, 10, 7

What can be concluded at the αα = 0.10 level ofsignificance?

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

H0:H0:  ? μ p  Select an answer < > ≥≤ ≠ =       

H1:H1:  ? μ p  Select an answer < ≤ ≠ ≥> =    

1. The test statistic ? t z  =  (please showyour answer to 3 decimal places.)
2. The p-value =  (Please show your answer to 4 decimalplaces.)
3. The p-value is ? ≤ >  αα
4. Based on this, we should Select an answer fail to reject rejectaccept  the null hypothesis.
5. Thus, the final conclusion is that ...
   • The data suggest the population mean is not significantly lessthan 10 at αα = 0.10, so there is enough evidence to conclude thatthe population mean number of paintings that are in teachers'houses is equal to 10.
   • The data suggest the populaton mean is significantly less than10 at αα = 0.10, so there is enough evidence to conclude that thepopulation mean number of paintings that are in teachers' houses isless than 10.
   • The data suggest that the population mean number of paintingsthat are in teachers' houses is not significantly less than 10 atαα = 0.10, so there is not enough evidence to conclude that thepopulation mean number of paintings that are in teachers' houses isless than 10.
6. Interpret the p-value in the context of the study.
   • If the population mean number of paintings that are inteachers' houses is 10 and if you survey another 14 teachers, thenthere would be a 0.32% chance that the population mean number ofpaintings that are in teachers' houses would be less than 10.
   • If the population mean number of paintings that are inteachers' houses is 10 and if you survey another 14 teachers, thenthere would be a 0.32% chance that the sample mean for these 14teachers would be less than 8.57.
   • There is a 0.32% chance that the population mean number ofpaintings that are in teachers' houses is less than 10.
   • There is a 0.32% chance of a Type I error.
7. Interpret the level of significance in the context of thestudy.
   • If the population mean number of paintings that are inteachers' houses is less than 10 and if you survey another 14teachers, then there would be a 10% chance that we would end upfalsely concuding that the population mean number of paintings thatare in teachers' houses is equal to 10.
   • If the population mean number of paintings that are inteachers' houses is 10 and if you survey another 14 teachers, thenthere would be a 10% chance that we would end up falsely concudingthat the population mean number of paintings that are in teachers'houses is less than 10.
   • There is a 10% chance that teachers are so poor that they areall homeless.
   • There is a 10% chance that the population mean number ofpaintings that are in teachers' houses is less than 10.