(1.)

\fUse the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables. r= 0.915, where x = distance in miles and y = fare in dollars What is the value of the coefficient of determination? The coefficient of determination is (Round to four decimal places as needed.)\fc. Find the indicated prediction interval. (Round to four decimal places as needed.)Listed below are altitudes (thousands of feet) and outside air temperatures ("F) recorded during a flight. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 95% confidence level with the altitude of 6327 ft (or 6.327 thousand feet). Altitude 2 12 15 20 28 31 32 Temperature 55 31 25 - 9 -25 -41 - 55 a. Find the explained variation. (Round to two decimal places as needed. )State the conclusion. Ho- There sufficient evidence to warrant rejection of the claim that the days of the week are selected with a uniform distribution. It that all days have the same chance of being selected.A random sample of 795 subjects was asked to identify the day of the week that is best for quality family time. Consider the claim that the days of the week are selected with a uniform distribution so that all days have the same chance of being selected. The table below shows goodness-of-fit test results from the claim and data from the study. Test that claim using either the critical value method or the P-value method with an assumed significance level of a = 0.05. Test statistic, Num Categories 7 2720.573 Degrees of freedom 6 Critical y 12.592 Expected Freq 113.5714 P-Value 0.0000 Determine the null and alternative hypotheses. Ho H\fState the conclusion. Ho- There sufficient evidence to warrant rejection of the claim that the four categories are equally likely. The results to support the expectation that the frequency for the first category is disproportionately high.Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion. A person randomly selected 100 checks and recorded the cents portions of those checks. The table below lists those cents portions categorized according to the indicated values. Use a 0.05 significance level to test the claim that the four categories are equally likely. The person expected that many checks for whole dollar amounts would result in a disproportionately high frequency for the first category, but do the results support that expectation? Cents portion of check 0-24 25-49 50-74 75-99 Number 30 26 18 26 Click here to view the chi-square distribution table. The test statistic is (Round to three decimal places as needed.)Area to the Right of the Critical Value Degrees of Freedom 0.995 0.99 0.975 0.95 0.90 0.10 0.001 0.004 0.016 2.706 N - 0.010 0.020 0.051 0.103 0.211 4.605 0.072 0.115 0.216 0.352 0.584 6.251 0.207 0.297 0.484 0.711 1.064 7.779 0.412 0.554 0.831 1.145 1.610 9.236 0.676 0.872 1.237 1.635 2.204 10.645 0.989 1.239 1.690 2.167 2.833 12.017 1.344 1.646 2.180 2.733 3.490 13.362 1.735 2.088 2.700 3.325 4.168 14.684 2.156 2.558 3.247 3.940 4.865 15.987