Given P(A) = 0.22, P(B) = 0.26, and P(B|A) = 0.26, are A and B independent or dependent?
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Q: 8Given that p(A | B)=0, and p(A)=.15, (a) independent? (b) exclusive? are A and B
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Q: Given P(A) = 0.21, P(B) = 0.24, and P(B|A) = 0.24, are A and B independent or dependent?
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Given P(A) = 0.22, P(B) = 0.26, and P(B|A) = 0.26, are A and B independent or dependent?
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- If P( A) = .40, P( B) = .30, and P AOB) = .15, then P( AI B) is .375 .12 .50 .045The following table was generated from the sample data of 1010 junior high students regarding the average number of hours they are unsupervised per night, the average number of hours they play video games per night, and their final grades in their math class. The dependent variable is the final grade, the first independent variable (x1x1) is the number of hours unsupervised each night, and the second independent variable (x2x2) is the number of hours of video games each night. Coefficients Standard Error t-Stat p-value Intercept 57.968435 7.227955 8.020032 0.000201 Hours Unsupervised 5.131630 1.314283 3.904510 0.007943 Hours Playing Video Games 1.067855 1.615039 0.661194 0.533040 Write the multiple regression equation for the computer output given. Round your answers to three decimal places.According to a recent survey of first-year high school students, 28% chew gum daily. The students were also asked if they had recently gotten a cavity filled at the dentist. Of the 47% of first-year students who responded that they had a cavity recently filled, only 39% chewed gum daily. Is chewing gum independent of having a cavity filled recently? Yes, P(Gum) = P(Gum|Cavity). Yes, P(Gum) = P(Cavity|Gum). No, P(Gum) ≠ P(Gum|Cavity). No, P(Gum) ≠ P(Cavity|Gum).
- A random group of customers at a fast food chain were asked whether they preferred hamburgers, chicken sandwiches, or fish sandwiches. The restaurant's marketing department claims that 45% of customers prefer hamburgers, 45% of the customers prefer chicken sandwiches, and 10% of the customers prefer fish sandwiches. Is there evidence to reject this hypothesis at = 0.05? Plans Hamburgers Chicken Fish Number of students 34 18 8 Group of answer choices A. There is evidence to reject the claim that the customers' preferences are distributed as claimed because the test value 17.2> 5.481 B. There is not evidence to conclude the claim that the customers' preferences are distributed as claimed because the test value 5.481 < 7.815 C. There is not evidence to reject the claim that the customers' preferences are distributed as claimed because the test value 5.481 < 5.991 D. There is evidence to conclude the claim that the customers' preferences are…An automobile service facility specializing in engine tune-ups knows that 60% of all tune-ups are done on four-cylinder automobiles, 30% on six-cylinder automobiles, and 10% on eight-cylinder automobiles. Let X = the number of cylinders on the next car to be tuned. What is the pmf of X?Darley and Latané (1968) recorded the speed with which subjects summoned help for a person in trouble. Subjects thought either that they were the only one listening to the person (Group 1, n 5 13), that one other person was listening (Group 2, n 5 26), or that four other people were listening (Group 3, n 5 13). The dependent variable was the speed with which the person summoned help (5 1/time × 100). The mean speed scores for the three groups were 0.87, 0.72, and 0.51, respectively. The MSerror was 0.053. Reconstruct the analysis of variance summary table. What can you conclude?
- Given P(A) = 0.27, P(B) = 0.27, and P(B|A) = 0.21, are A and B independent or dependent?In a recent study, 50 males used a new weight-loss supplement, and 39 of them experienced weight loss a 100 females used the same supplement, and 66 of them experienced weight loss after two weeks. Fill in the blanks below to make the most reasonable statement possible. The new weight-loss supplement was more effective on (Choose one) ▼ in the study. That is because only % of them failed to lose weight after two weeks, whereas % of the (Choose one) failed to lose weight after two weeks.A beverage company surveyed 310 customers about their favorite type of weather and preferred beverage. The results are displayed in the table. Water Coffee Tea Soft Drink Sunny 28 44 16 36 Stormy 14 22 18 8 Snowy 21 21 33 12 27 Cloudy 7 11 9 4 Is preferring water independent of favoring snowy weather? Justify mathematically. Yes, because 0.068 = (0.226)(0.300) Yes, because 0.021 (0.226)(0.300) No, because 0.068 = (0.226)(0.300) No, because 0.021 # (0.226)(0.300)
- Nathan has been quietly practicing his skills and is now an amazing dart player. At this point, he has a 70% chance to hit the bull’s eye on any given throw! Let’s assume that each throw of the dart is independent of another. Nathan decides to test himself and enters a Friday night dart tournament, he will have to throw 120 darts across several matches, let B = the number of bull’s eyes that he hits. 1.Check the criteria to show that B is a binomial random variable. 2.Check the conditions for using a Normal approximation in this setting 3. What’s the probability that Nathan will hit at least 75 bull’s eyes across the tournament?A physician wants to see if there was a difference in the average smokers' daily cigarette consumption after wearing a nicotine patch. The physician set up a study to track daily smoking consumption. In the study, the patients were given a placebo patch that did not contain nicotine for 4 weeks, then a nicotine patch for the following 4 weeks. Test to see if there was a difference in the average smoker's daily cigarette consumption using α = 0.01. The hypotheses are: H0 : μD = 0 H1 : μD ≠ 0 t-Test: Paired Two Sample for Means Placebo Nicotine Mean 18.75 12.3125 Variance 66.599 34.6667 Observations 16 16 Pearson Correlation 0.6105 Hypothesized Mean Difference 0 df 15 t Stat 3.5481 P(T<=t) one-tail 0.0126 t Critical one-tail 2.6025 P(T<=t) two-tail 0.0252 t Critical two-tail 2.9467 What is the correct p-value? Question 1 options:…Biologists in Minnesota are interested in determining if there is a difference in the invasion rate of Asian Carp (which can be detrimental to the environment) between the Mississippi River and Lake Mille Lacs. In the Mississippi River, it was found that 206 of 579 fish caught were Asian Carp. In Lake Mille Lacs, 28 of 132 fish caught were Asian Carp. Let p, = the true proportion of Asian Carp in the Mississippi River and let p2 = the true proportion of Asian Carp in Lake Mille Lacs. A test of Ho: P₁ = P2 vs. Ha: P₁ P₂ resulted in a p-value of 0.0015. Which of the following is a correct conclusion? (A) The test is not appropriate, since the researchers should have conducted a one-sided test. (B) The test is not appropriate, since the sample size is too small to conduct an inference test for proportions. (C) The test is not appropriate, since the two sample sizes are very different. (D) The p-value of this test is large, indicating we have sufficient evidence to conclude that a…