Question

The average house has 10 paintings on its walls. Is the mean smaller 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.

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

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 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 < ≤ ≠ ≥ > =    

3. The test statistic ? t z  =  (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 the population mean is not significantly less than 10 at αα = 0.10, so there is enough evidence to conclude that the population mean number of paintings that are in teachers' houses is equal to 10.
   • The data suggest the populaton mean is significantly less than 10 at αα = 0.10, so there is enough evidence to conclude that the population mean number of paintings that are in teachers' houses is less than 10.
   • The data suggest that the population mean number of paintings that are in teachers' houses is not significantly less than 10 at αα = 0.10, so there is not enough evidence to conclude that the population mean number of paintings that are in teachers' houses is less than 10.
8. Interpret the p-value in the context of the study.
   • If the population mean number of paintings that are in teachers' houses is 10 and if you survey another 14 teachers, then there would be a 0.32% chance that the population mean number of paintings that are in teachers' houses would be less than 10.
   • If the population mean number of paintings that are in teachers' houses is 10 and if you survey another 14 teachers, then there would be a 0.32% chance that the sample mean for these 14 teachers would be less than 8.57.
   • There is a 0.32% chance that the population mean number of paintings that are in teachers' houses is less than 10.
   • There is a 0.32% chance of a Type I error.
9. Interpret the level of significance in the context of the study.
   • If the population mean number of paintings that are in teachers' houses is less than 10 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 10.
   • If the population mean number of paintings that are in teachers' houses is 10 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 less than 10.
   • There is a 10% chance that teachers are so poor that they are all homeless.
   • There is a 10% chance that the population mean number of paintings that are in teachers' houses is less than 10.

Answer 1

(a)

For this study, we should use t-test for a population mean

(b)

H0: 10

HA: 10

(a)

From the given data, the following statistics are calculated:

n = 14

= 8.5714

s = 1.6508

Test Statistic is given by:

(b)

By Technology

p - value = 0.0032

(c)

p - value <

(d)

Correct option:

reject   the null hypothesis

(e)

Correct option:

The data suggest the populaton mean is significantly less than 10 at α = 0.10, so there is enough evidence to conclude that the population mean number of paintings that are in teachers' houses is less than 10.

(f)

Correct option:

If the population mean number of paintings that are in teachers' houses is 10 and if you survey another 14 teachers, then there would be a 0.32% chance that the population mean number of paintings that are in teachers' houses would be less than 10.

(g)

If the population mean number of paintings that are in teachers' houses is 10 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 less than 10.