The average house has 15 paintings on its walls. Is the mean smaller for houses owned by teachers? The data show the results of a survey of 11 teachers who were asked how many paintings they have in their houses. Assume that the distribution of the population is normal.

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

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

For this study, we should use

The null and alternative hypotheses would be:

H0:H0:

H1:H1:

The test statistic     =  (please show your answer to 3 decimal places.)

The p-value =  (Please show your answer to 4 decimal places.)

The p-value is     αα

Based on this, we should      the null hypothesis.

Thus, the final conclusion is that ...

The data suggest that the population mean number of paintings that are in teachers' houses is not significantly less than 15 at αα = 0.10, so there is insufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is less than 15.

The data suggest the populaton mean is significantly less than 15 at αα = 0.10, so there is sufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is less than 15.

The data suggest the population mean is not significantly less than 15 at αα = 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.

Interpret the p-value in the context of the study.

If the population mean number of paintings that are in teachers' houses is 15 and if you survey another 11 teachers, then there would be a 8.34% chance that the sample mean for these 11 teachers would be less than 14.27.

There is a 8.34% chance that the population mean number of paintings that are in teachers' houses is less than 15.

There is a 8.34% chance of a Type I error.

If the population mean number of paintings that are in teachers' houses is 15 and if you survey another 11 teachers, then there would be a 8.34% chance that the population mean number of paintings that are in teachers' houses would be less than 15.

Interpret the level of significance in the context of the study.

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 15 and if you survey another 11 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 less than 15.

There is a 10% chance that the population mean number of paintings that are in teachers' houses is less than 15.

If the population mean number of paintings that are in teachers' houses is less than 15 and if you survey another 11 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.

Question

The average house has 15 paintings on its walls. Is the mean smaller for houses owned by teachers? The data show the results of a survey of 11 teachers who were asked how many paintings they have in their houses. Assume that the distribution of the population is normal.

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

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

For this study, we should use
The null and alternative hypotheses would be:

H0:H0:

H1:H1:

The test statistic = (please show your answer to 3 decimal places.)
The p-value = (Please show your answer to 4 decimal places.)
The p-value is αα
Based on this, we should the null hypothesis.
Thus, the final conclusion is that ...
- The data suggest that the population mean number of paintings that are in teachers' houses is not significantly less than 15 at αα = 0.10, so there is insufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is less than 15.
- The data suggest the populaton mean is significantly less than 15 at αα = 0.10, so there is sufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is less than 15.
- The data suggest the population mean is not significantly less than 15 at αα = 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.
Interpret the p-value in the context of the study.
- If the population mean number of paintings that are in teachers' houses is 15 and if you survey another 11 teachers, then there would be a 8.34% chance that the sample mean for these 11 teachers would be less than 14.27.
- There is a 8.34% chance that the population mean number of paintings that are in teachers' houses is less than 15.
- There is a 8.34% chance of a Type I error.
- - If the population mean number of paintings that are in teachers' houses is 15 and if you survey another 11 teachers, then there would be a 8.34% chance that the population mean number of paintings that are in teachers' houses would be less than 15.
- Interpret the level of significance in the context of the study.
  - 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 15 and if you survey another 11 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 less than 15.
  - There is a 10% chance that the population mean number of paintings that are in teachers' houses is less than 15.
  - If the population mean number of paintings that are in teachers' houses is less than 15 and if you survey another 11 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.

Accepted Answer

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