Reference no: EM132339491

Question

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

17, 17, 16, 16, 16, 15, 13, 16, 14, 15, 13, 13, 16

What can be concluded at the α= 0.05 level of significance?

a.) for this study should we use the t-test or z-test?

b.) The null and alternative hypotheses would be:   

H₀:____ ____ ____

H₁:____ ____ ____

c.) The test statistic ____=_____(please show to 3 decimal places)

d.) the p-value=______please show to 4 decimal places

e.) the p value is_____

F.) Based on this we should either fail to reject, reject or accept the null hypothesis

g.) Thus, the final conclusion is that ...

1.) The data suggest the populaton mean is significantly more than 14 at α = 0.05, so there is sufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is more than 14.

2.) The data suggest the population mean is not significantly more than 14 at α = 0.05, so there is sufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is equal to 14.

3.) The data suggest that the population mean number of paintings that are in teachers' houses is not significantly more than 14 at α= 0.05, so there is insufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is more than 14.

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

1.) If the population mean number of paintings that are in teachers' houses is 14 and if you survey another 13 teachers then there would be a 0.74% chance that the sample mean for these 13 teachers would be greater than 15.15.

2.) If the population mean number of paintings that are in teachers' houses is 14 and if you survey another 13 teachers then there would be a 0.74% chance that the population mean number of paintings that are in teachers' houses would be greater than 14.

3.) There is a 0.74% chance of a Type I error.

4.) There is a 0.74% chance that the population mean number of paintings that are in teachers' houses is greater than 14.

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

1.) If the population mean number of paintings that are in teachers' houses is more than 14 and if you survey another 13 teachers, then there would be a 5% chance that we would end up falsely concuding that the population mean number of paintings that are in teachers' houses is equal to 14.

2.) If the population mean number of paintings that are in teachers' houses is 14 and if you survey another 13 teachers, then there would be a 5% chance that we would end up falsely concuding that the population mean number of paintings that are in teachers' houses is more than 14.

3.) There is a 5% chance that the population mean number of paintings that are in teachers' houses is more than 14.

4.) There is a 5% chance that teachers are so poor that they are all homeless.