The average house has 13 paintings on its walls. Is the mean larger for houses owned by teachers? The data show the results of a survey of 14 teachers who were asked how many paintings they have in their houses. Assume that the distribution of the population is normal.

12, 15, 15, 13, 16, 14, 15, 14, 13, 12, 12, 15, 16, 13

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

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

H0:H0: ? p Select an answer > = <

H1:H1: ? p Select an answer = > <

1. The test statistic ? z t = (please show your answer to 3 decimal places.)
2. The p-value = (Please show your answer to 4 decimal places.)
3. The p-value is ? >
4. Based on this, we should Select an answer reject accept fail to reject the null hypothesis.
5. Thus, the final conclusion is that ...
6. Interpret the p-value in the context of the study.
7. Interpret the level of significance in the context of the study.
   • If the population mean number of paintings that are in teachers' houses is 13 and if you survey another 14 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 more than 13.
   • There is a 10% chance that teachers are so poor that they are all homeless.
   • If the population mean number of paintings that are in teachers' houses is more than 13 and if you survey another 14 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 13.
   • There is a 10% chance that the population mean number of paintings that are in teachers' houses is more than 13.

• If the population mean number of paintings that are in teachers' houses is 13 and if you survey another 14 teachers then there would be a 1.56% chance that the sample mean for these 14 teachers would be greater than 13.93.
• There is a 1.56% chance that the population mean number of paintings that are in teachers' houses is greater than 13.
• If the population mean number of paintings that are in teachers' houses is 13 and if you survey another 14 teachers then there would be a 1.56% chance that the population mean number of paintings that are in teachers' houses would be greater than 13.
• There is a 1.56% chance of a Type I error.

• The data suggest the population mean is not significantly more than 13 at = 0.10, so there is sufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is equal to 13.
• The data suggest the populaton mean is significantly more than 13 at = 0.10, so there is sufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is more than 13.
• The data suggest that the population mean number of paintings that are in teachers' houses is not significantly more than 13 at = 0.10, so there is insufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is more than 13.