Need help with D and I, please The text describes a hypothesis test conducted to determine if the average number of paintings in teachers' homes is different from the general average of 10 paintings per house. The study uses a sample of 14 teachers, with the number of paintings in each house listed as follows: 10, 9, 13, 9, 10, 13, 12, 10, 12, 12, 12, 12, 11. The significance level for the test is set at α = 0.10.### Steps in the Hypothesis Test:a. **Study Methodology**: - **Choice**: The appropriate test to use for the analysis.b. **Hypothesis Formulation**: - **Null Hypothesis (H₀)**: Specifies that the population mean is equal to 10. - **Alternative Hypothesis (H₁)**: Suggests the population mean is different from 10.c. **Test Statistic Calculation**: - **Test Statistic (t)**: To be calculated to three decimal places.d. **P-value**: - **Result**: To be reported to four decimal places.e. **Comparison with Alpha Level**: - **Decision Rule**: Based on whether the p-value is less than α.f. **Conclusion**: - **Interpretation**: The outcome of the hypothesis test. - **Options for Interpretation**: 1. Data suggests the mean is significantly different from 10; null hypothesis rejected. 2. Data suggests no significant difference from 10; null hypothesis accepted. 3. Inconclusive; not significantly different from 10 but lacks evidence for rejection.g. **Contextual Interpretation of the P-value**: - Provides several interpretations of what the p-value represents, including the likelihood of sample means diverging from 10 under repeated sampling.h. **Level of Significance Interpretation**: - Contextualizes what a 10% significance level implies in terms of probability of making incorrect conclusions about the population mean.This text guides users on setting up, calculating, and interpreting the results of a hypothesis test with a focus on practical application and statistical reasoning.

The number of paintings on the wall of 14 surveyed teachers (i.e., n=14) are:10, 9, 13, 13, 9, 10,…

The average house has 10 paintings on its walls. Is the mean different 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. 10, 9, 13, 13, 9, 10, 13, 12, 10, 12, 12, 12, 12, 11 What can be concluded at the a= 0.10 level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho: H₁: Select an answer Select an answer c. The test statistic d. The p-value= e. The p-value is ? a f. Based on this, we should Select an answer the null hypothesis. g. Thus, the final conclusion is that ... (please show your answer to 3 decimal places.) (Please show your answer to 4 decimal places.) O The data suggest the populaton mean is significantly different from 10 at a = 0.10, so there is sufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is different from 10. O The data suggest the population mean is not significantly different from 10 at a = 0.10, so there is sufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is equal to 10. O The data suggest that the population mean number of paintings that are in teachers' houses is not significantly different from 10 at a = 0.10, so there is insufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is different from 10. h. Interpret the p-value in the context of the study. O There is a 0.53% chance that the population mean number of paintings that are in teachers houses is not equal to 10. O 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 0.53% chance that the population mean would either be less than 9 or greater than 11. O 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 0.53% chance that the sample mean for these 14 teachers would either be less than 9 or greater than 11. O There is a 0.53% chance of a Type I error. i. Interpret the level of significance in the context of the study. O 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 different from 10. O If the population mean number of paintings that are in teachers' houses is different from 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. O 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 different from 10.