Consider the data. X; 2 6 9 13 20 YI 9 20 10 25 22 (a) What is the value of the standard error of the estimate? (Round your answer to three decimal places.) (b) Test for a significant relationship by using the t test. Use a = 0.05. State the null and alternative hypotheses. O Ho: B, + 0
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- Q1. An anthropologist wants to collect data to determine whether the two different cultural groups that occupy an isolated Pacific Island grow to be different heights. The results of his samples of the heights of adult females are as follows Do these samples constitute enough evidence to reject the null hypothesis that the heights of the two groups the same? Set alpha to .05.Suppose that you fitted the model E(y) = ?0 + ?1x1 + ?2x2 + ?3x3 to 15 data points and found F equal to 58.88. Do the data provide sufficient evidence to indicate that the model contributes information for the prediction of y? Test using a 5% level of significance. State the null and alternative hypotheses. H0: ?1 = ?2 = ?3 = 0 Ha: At least one of ?1, ?2, ?3 is not 0.H0: ?1 = ?2 = ?3 = 0 Ha: ?1 > ?2 > ?3 > 0 H0: ?1 < ?2 < ?3 Ha: ?1 = ?2 = ?3 = 0H0: ?1 = ?2 = ?3 Ha: At least one of ?1, ?2, ?3 is different from the others.H0: ?1 > ?2 > ?3 > 0 Ha: ?1 = ?2 = ?3 = 0 What is the test statistic? F = Find the rejection region. (Round your answer to two decimal places.) F > State your conclusion. H0 is rejected. There is insufficient evidence to indicate that the model contributes information for the prediction of y.H0 is not rejected. There is insufficient evidence to indicate that the model contributes information for the prediction of y. H0 is…Complete a-c for c do we reject or accept the p-value due to sufficient or insufficient evidence?
- An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola. Beverage Sample Size Sample Mean Sample SD Strawberry Drink 10 535 24 Cola 10 559 15 Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value. (Use ? = 0.05.) State the relevant hypotheses. (Use ?1 for the strawberry drink and ?2 for the cola.) H0: ?1 − ?2 = 0Ha: ?1 − ?2 ≥ 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 ≠ 0 H0: ?1 − ?2 = 0Ha: ?1 − ?2 < 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 > 0 Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. Reject H0. The data suggests that cola has a higher average compression strength than the strawberry drink.Reject H0. The…Given the Data:Test the hypothesis that p(rho)xy is not equal to 0 at the 0.05 level of significance.T/F question the MSE(theta) for an unbiased estimator is given by its variance.
- A major credit card company is interested in whether there is a linear relationship between its internal rating of a customer’s credit risk and that of an independent rating agency. The company collected a random sample of 200 customers and used the data to test the claim that there is a linear relationship. The following hypotheses were used to test the claim. H0:β1=0Ha:β1≠0 The test yielded a t-value of 3.34 with a corresponding p-value of 0.001. Which of the following is the correct interpretation of the p-value? If the alternative hypothesis is true, the probability of observing a test statistic at least as extreme as 3.34 is 0.001. If the alternative hypothesis is true, the probability of observing a test statistic at least as extreme as 3.34 is 0.001. A If the alternative hypothesis is true, the probability of observing a test statistic of 3.34 or greater is 0.001. If the alternative hypothesis is true, the probability of observing a test statistic of 3.34 or greater…Consider the data. xi 2 6 9 13 20 yi 6 19 9 28 22 (a) What is the value of the standard error of the estimate? (Round your answer to three decimal places.) ?? (b) Test for a significant relationship by using the t test. Use ? = 0.05. State the null and alternative hypotheses. -H0: ?0 = 0Ha: ?0 ≠ 0 -H0: ?0 ≠ 0Ha: ?0 = 0 -H0: ?1 ≠ 0Ha: ?1 = 0 -H0: ?1 ≥ 0Ha: ?1 < 0 -H0: ?1 = 0Ha: ?1 ≠ 0 Find the value of the test statistic. (Round your answer to three decimal places.) ?? Find the p-value. (Round your answer to four decimal places.) p-value = ?? State your conclusion. -Do not reject H0. We cannot conclude that the relationship between x and y is significant. -Do not reject H0. We conclude that the relationship between x and y is significant. - Reject H0. We cannot conclude that the relationship between x and y is significant. -Reject H0. We conclude that the relationship between x and y is significant. (c) Use the F test to test for a…D. Which video streaming platform(s) has(have) the highest median time spent by its patrons? E. Which video streaming platform(s) has(have) the most varied lower 25% of observations? F. Which video streaming platform(s) has(have) at least 75% of its observations less than or equal to 150? G. The upper extreme observation of Disney+ is approximately equal to the upper extreme of which video streaming platform(s)?
- For the following setting, (a) describe the parameter of interest, and (b) state the appropriate hypotheses for a significance test. According to the website sleepdeprivation.com, 85% of teens are getting less than eight hours of sleep a night. Jannie wonders whether this result holds in her large high school. She asks an SRS of 100 students at the school how much sleep they get on a typical night. In all, 75 of the responders said less than 8 hours.Use the standard error to construct a approximate prediction interval for Y using an alpha of 5%. (Round your answer to 3 decimal places.) Obs Assessed Floor Offices Entrances Age Freeway 1 1796 4790 4 2 8 0 2 1544 4720 3 2 12 0 3 2094 5940 4 2 2 0 4 1968 5720 4 2 34 1 5 1567 3660 3 2 38 1 6 1878 5000 4 2 31 1 7 949 2990 2 1 19 0 8 910 2610 2 1 48 0 9 1774 5650 4 2 42 0 10 1187 3570 2 1 4 1 11 1113 2930 3 2 15 1 12 671 1280 2 1 31 1 13 1678 4880 3 2 42 1 14 710 1620 1 2 35 1 15 678 1820 2 1 17 1 16 1585 4530 2 2 5 1 17 842 2570 2 1 13 0 18 1539 4690 2 2 45 0 19 433 1280 1 1 45 1 20 1268 4100 3 1 27 0 21 1251 3530 2 2 41 1 22 1094 3660 2 2 33 0 23 638 1110 1 2 50 1 24 999 2670 2 2 39 1 25 653 1100 1 1 20 1 26 1914 5810 4 3 17 0 27 772 2560 2 2 24 0 28 890 2340 3 1 5 0 29 1282 3690 2 2 15 1 30 1264 3580 3 2 27 0 31 1162 3610 2 1 8 1 32 1447 3960 3 2 17 0Which of the following eta-squared results would indicate a very weak relationship between the dependent and independent variables? .15 .35 65 .95