Which assumption of the least-squares estimation is violated when the error term is heteroscedastic? State verbally and formally. b. Which test would you recommend to verify if heteroscedasticity exists? What measures would you take to address the consequences of heteroscedasticity? с.
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- (d) Use a t-test to test if the relationship between years of experience and income is statistically significant at the 0.05 level of significance. State the null and alternative hypotheses. O Ho: B₁ ≥ 0 H₂: B₁< < 0 Ho: B₁ = 0 Ha: B₁ * 0 O Ho: B₁ * 0 Ha: B₁ = 0 о ново = 0 Ha: Bo # 0 Ho Bo # 0 Ha: Bo Find the value of the test statistic for the t-test. (Round your answer to three decimal places.) = = 0 Find the p-value. (Round your answer to four decimal places.) p-value What is your conclusion? O Reject Ho. We conclude that the relationship between years of experience and income is significant. O Do not reject Ho. We cannot conclude that the relationship between years of experience and income is significant. O Reject Ho. We cannot conclude that the relationship between years of experience and income is significant. O Do not reject Ho. We conclude that the relationship between years of experience and income is significant. (e) Calculate the coefficient of determination. (Round your…What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data. 16.1 22.7 25.3 1.98 32.2 38.3 51.3 20.5 y 2.78 1.88 1.03 0.75 2.38 2.20 (a) Find Ex, Ey, Ex, Ey", Exy, and r. (Round r to three decimal places.) Ex= Ey= Ey? - Exy = (b) Use a 1% level of significance to test the claim that p < 0. (Round your answers to two decimal places.) critical t= Conclusion O Fail to reject the null hypothesis. There is sufficient evidence that p < 0. O Fail to reject the null hypothesis. There is insufficient evidence that p < 0. Reject the null hypothesis. There is sufficient evidence that p < 0. Reject the null hypothesis.…What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data.x 12.1 26.3 32.2 38.3 51.3 20.5 22.7y 2.48 2.18 1.48 1.03 0.75 2.38 2.20 a) Find the predicted optimal time in hours for a dive depth of x = 22 meters. (Round your answer to two decimal places.)______ hr b) Find an 80% confidence interval for y when x = 22 meters. (Round your answers to two decimal places.)lower limit= ____ hrupper limit =____hr c) Find a 90% confidence interval for ? and interpret its meaning. (Round your answers to three decimal places.)lower limit =upper limit=
- weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again, and the net gain in grams is recorded. Using a significance level of 0.05, test the hypothesis that the three formulas produce the same mean weight gain.H0: μ1 = μ2 = μ3Ha: At least two of the means differ from each other Forumla A Forumla B Forumla C 51 39.4 53.6 55.8 55.1 42.4 53.8 33.1 50.1 43.2 58.7 40.4 42.1 40.4 46.9 50.1 19 45.6 59.5 43.2 48.7 35.4 32.2 49.5 45.2 16.4 56.1 Run a one-factor ANOVA with α=0.05. Report the F-ratio to 4 decimal places and the p-value to 4 decimal places.F = p-value = Based on the p-value, what is the conclusion Reject the null hypothesis: at least one of the group means is different Fail to reject the null hypothesis: not sufficient evidence to suggest the group means are differentA researcher in nursing wanted to know if the recovery of patients was quicker when some received additional in-home care whereas others received the standard amount. Would you perform a t-test of independent means or a t-test of dependent means?What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y optimal time in hours. A random sample of divers gave the following data. 15.1 23.3 32.2 38.3 51.3 20.5 22.7 2.48 2.38 1.48 1.03 0.75 2.38 2.20 (a) Find Ex, Ey, Ex², Ey², Exy, and r. (Roundr to three decimal places.) Ex = 203.4 Ey = 12.7 Ex2 = 0.001 Ey? = 0.002 Exy = 931.638 r= -0.9655 (b) Use a 1% level of significance to test the claim that p < 0. (Round your answers to two decimal places.) t = -8.29 critical t = -3.36 Conclusion O Reject the null hypothesis. There is insufficient evidence that p < 0. Reject the null hypothesis. There is sufficient evidence that p < 0. Fail to reject the null hypothesis. There is…
- What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data. 15.1 26.3 31.2 38.3 51.3 20.5 22.7 y 2.68 2.38 1.48 1.03 0.75 2.38 2.20 (a) Find Ex, Ey, Ex², Ey², Exy, and r. (Round r to three decimal places.) Σχ = Ey = Ex? = Ey? = Σχy r = (b) Use a 1% level of significance to test the claim that p < 0. (Round your answers to two decimal places.) t = critical t = Conclusion O Fail to reject the null hypothesis. There is insufficient evidence that p < 0. O Fail to reject the null hypothesis. There is sufficient evidence that p < 0. O Reject the null hypothesis. There is insufficient evidence that p < 0. O…The manager of the city pool has scheduled extra lifeguards to be on staff for Saturdays. However, he suspects that Fridays may be more popular than the other weekdays as well. If so, he will hire extra lifeguards for Fridays, too. In order to test his theory that the daily number of swimmers varies on weekdays, he records the number of swimmers each day for the first week of summer. Test the manager’s theory at the 0.01 level of significance. Swimmers at the City Pool Monday Tuesday Wednesday Thursday Friday Number 64 46 41 56 70 Copy Data Step 2 of 4 : Calculate the expected value for the number of swimmers on Tuesday. Enter your answer as a fraction or a decimal rounded to three decimal places.What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data. 16.1 23.3 29.2 38.3 51.3 20.5 22.7 2.68 2.18 1.88 1.03 0.75 2.38 2.20 (c) Find S, a, and b. (Round your answers to five decimal places.) e' Se a = b = (d) Find the predicted optimal time in hours for a dive depth of x = 38 meters. (Round your answer to two decimal places.) hr (e) Find an 80% confidence interval for y when x = 38 meters. (Round your answers to two decimal places.) lower limit hr upper limit hr (f) Use a 1% level of significance to test the claim that ß < 0. (Round your answers to two decimal places.) t = critical t = (g) Find a 90%…
- Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 133133 to 190190 cm and weights of 3737 to 150150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x overbarxequals=168.08168.08 cm, y overbaryequals=81.5781.57 kg, requals=0.3130.313, P-valueequals=0.0020.002, and ModifyingAbove y with caretyequals=negative 108−108plus+1.121.12x. Find the best predicted value of ModifyingAbove y with carety (weight) given an adult male who is 169169 cm tall. Use a 0.050.05 significance level. The best predicted value of ModifyingAbove y with carety for an adult male who is 169169 cm tall is (answer) kg. (Round to two decimal places as needed.)In recent years, approximately 55% of eligible voters take the time to vote in presidential elections. A poll based on a random sample of 200 eligible voters finds that 128 plan to vote in the next presidential election. Does this data provide convincing evidence at the ?α = 0.05 level that the proportion of eligible voters who will take time to vote in the next presidential election differs from 0.55?What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data. x 16.1 26.3 29.2 38.3 51.3 20.5 22.7 y 2.68 1.98 1.48 1.03 0.75 2.38 2.20 (b) Use a 1% level of significance to test the claim that ? < 0. (Round your answers to two decimal places.) t = critical t =
