The average house has 10 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. 9, 13, 11, 10, 12, 13, 9, 11, 12, 12, 11, 13, 10 What can be concluded at the a = 0.05 level of significance? a. For this study, we should use t-test for a population mean b. The null and alternative hypotheses would be: Ho: uv= 10 H: [µv > 10 c. The test statistic tv 3.711 (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) %3! e. The p-value is ?v a f. Based on this, we should Select an answerv the null hypothesis. g. Thus, the final conclusion is that O The data suggest the populaton mean is significantly more than 10 at a = 0.05, so there is sufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is more than 10. O The data suggest the population mean is not significantly more than 10 at a = 0.05, 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 more than 10 at a = 0.05, so there is insufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is more than 10. %3D h. Interpret the p-value in the context of the study. O f the population mean number of paintings that are in teachers' houses is 10 and if you survey another 13 teachers then there would be a 0.44% chance that the population mean number of paintings that are in teachers' houses would be greater than 10. O There is a 0.44% chance of a Type I error.

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Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.