Which of the following is(are) TRUE if the coefficient of determination between the response and the predictor variables is 0.81 based on a random sample of size n.
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- A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 75%.At a .05 level of significance, it can be concluded that the proportion of the population in favor of candidate A is _____.A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly different than 75%. At a .05 level of significance, it can be concluded that the proportion of the population in favor of candidate A is significantly different than 80% significantly different than 75% not significantly different than 80% not significantly greater than 80% not significantly different than 75%Researchers conducted trials to investigate the effects of color on creativity. Subjects with a red background were asked to think of creative uses for a brick; other subjects with a blue background were given the same task. Responses were scored by a panel of judges and results from scores of creativity are given in the accompanying table. Higher scores correspond to more creativity. The researchers make the claim that "blue enhances performance on a creative task." Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b). Click the icon to view the summary statistics. a. Use a 0.01 significance level to test the claim that blue enhances performance on a creative task. What are the null and alternative hypotheses? OA. Ho: H₁ H₂ H₁: H₁ H₂ OC. Ho: H₁ H₂ H₁: H₁ H₂ The test statistic, t, is (Round to two decimal places as needed.) The…
- A toll collector wonders if drivers are equally likely to choose each of the three lanes at his toll booth. He selects a random sample of 465 drivers that approach the booth when all three lanes are empty, so that the driver's choice isn't influenced by the cars already at the booth. The table below summarizes the data: Lane Left Center Right Number of drivers 137 159 169 Which of the following is an appropriate alternative hypothesis for addressing this question? Drivers are not equally likely to choose each of the three lanes O The observed number of drivers choosing each lane is equal. The observed number of drivers choosing each lane is different from the expected numbers. The proportion of drivers choosing each of the three lanes are equal. O The proportion of drivers choosing each of the three lanes are all different.An official of a large car manufacturing company wanted to study the relationship between an employee's age and the number of absences. For this, a random sample of 10 randomly selected employees was collected and the following data was obtained. The material: age 40 28 34 27 21 38 19 55 31 35 number of absences 1 6 6 9 12 4 13 2 5 3 (a) Predict the number of absenteeism for a 42-year-old employee.(b) Determine the 95% prediction interval for the number of absences for the employee in (a).A veterinary hospital manager suspects that pet owners visit the veterinarian less than 3 times a year. To verify this suspicion, he hires a market research agency that takes a random sample of 64 clients and asks them the number of times they go to the veterinarian per year. The decision the market researcher makes is that if 2.8, then he will have sufficient evidence to say that the manager's suspicion is true. Assume that the frequency of visiting the veterinarian has a standard deviation of 1.02. a) Write the null hypothesis and the alternative hypothesis in this case. b) What is the rejection region used by the investigator? c) What is the probability of type I. error if this rejection region is used? d) If the true mean of the number of visits to the veterinarian is = 2.7, what is the probability of type II error? e) If the true mean of the number of visits to the veterinarian is = 2.7, what is the power of the test? f) If the true mean of the number of visits to…
- Determine if the samples are independent or related. Two formulations of a new whitening soap are compared to their whitening effect. A random sample of 40 potential users of the soap is selected. Each person uses a randomization mechanism to determine which formulation is applied on the left arm so that the other formulation is applied on the right arm. After two weeks, they measured the effect of each formulation.2.24 Exit poll: Edison Research gathered exit poll results from several sources for the Wisconsin recall election of Scott Walker. They found that 53% of the respondents voted in favor of Scott Walker. Additionally, they estimated that of those who did vote in favor for Scott Walker, 33% had a college degree, while 44% of those who voted against Scott Walker had a college degree. Suppose we randomly sampled a person who participated in the exit poll and found that he had a college degree. What is the probability that he voted in favor of Scott Walker?A cat-lover claims that cats are just as smart as dogs. In order to back this claim up with some evidence she organizes a study at a large local pet daycare center. A random sample of 40 cats are selected and a random sample of 40 dogs are selected. Each of the selected animals is given one hour with a trainer in which the trainer attempts to teach them to roll over. Upon conclusion of the training, the proportion of dogs and proportion of cats that have learned this skill is computed. The trainer reports that she is 90% confident that the true difference in the proportion of all dogs and all cats (pD – pC) that can learn this skill with one hour of training is between –0.05 to 0.28. Which of the following conclusions can be made based upon this confidence interval? (A) Because most of the values in the confidence interval are positive, this proves that dogs are smarter than cats. (B) Because the point estimate of the confidence interval is positive, there is convincing evidence…