Section 10.1 Learning Check|Use the following to answer the questions 1-6. <br> Do children's fear level change over time, and if so, in what whys? Little research has been done on the prevalence and persistance of fears in children. in 1989 two researhers surveyed a group of 94 third and fourth grade children., asking them to rate their level of fearfulness about a variety of situations. Two years later the children again completed the same survey. The researchers computed the mean fear rating for each child in both years and were interested in the relation between these ratings. They then used the following simple linear regression model <br> <center> 1991 Mean Rating = b<sub>0</sub>+b<sub>1</sub>(1989 Mean rating)+e<sub>i</sub>.</center> <br> This model was fit to the data by using the methoid of least squares. The following results were obtained from the statistical software: <br> R<sup>2</sup>=0.274<br> s=0.2374<br> <table><tr><td>Variable</td><td>Parameter est.</td><td>Std. Error of Par. Est.</td></tr><tr><td>Constant</td><td>0.877917</td><td>0.1184</td></tr><tr><td>1989 Mean Rating</td><td>0.397911</td><td>0.0676</td></tr></table>|Please enter your Full Name:|Your Email Address:|Your ID Number or Password:|The explanatory variable in this study is # 1989 mean fear ratings %% 1991 mean fear ratings %% the difference in the mean fear ratings for the two years %% the particular group of 94 children used in the study. %%|The quantity s=0.2374 is an estimate of the population standard deviation in the simple linear regression model. The degress of freedom for s are # 92 %% 93 %% 94 %% none of the above. %%|Suppose that the researchers wants to test the hypothesis that the slope is different than 0. The value of the t statistic for this test is # 0.27 %% 0.40 %% 5.89 %% 7.41 %%|A 95% confidence interval for the slope in the simple regression model is (approximately) # 0.88+-0.12 %% 0.88+-0.14 %% 0.40+-0.07 %% 0.40+-0.14 %%|The correlation between the 1989 and 1991 mean fear ratings is # 0.274 %% 0.400 %% 0.523 %% 0.632 %%|Suppose we wish to predict the 1991 mean fear rating for a child who had a 1989 mean fear rating of 1.5. A 95% interval for this prediction is # (1.418, 1.531) %% (1.000, 1.950) %% 1.4748+-0.0284 %% Not enough information given %%