You may need to use the appropriate technology to answer this question. A certain manufacturer is a producer of aluminum components for the avionics and automotive industries. At its plant, an engineer has conducted a quality-control test in which aluminum coils produced in all three shifts were inspected. The study was designed to determine if the population proportion of good parts was the same for all three shifts. Sample data follow. Production Shift Quality First Second Third Good 282 364 172 Defective 18 36 28 (a) Using a 0.05 level of significance, conduct a hypothesis test to determine if the population proportion of good parts is the same for all three shifts. State the null and alternative hypotheses. O Hạ: Not all population proportions are equal. H: P, = P2" Ps O Ho: At least two population proportions are equal. H: P, P2 P3 O Hại P,• P2 P3 H: All population proportions are equal. O Moi P = P2- P3 H: Not all population proportions are equal.

A company produces scooters used by small businesses that find them convenient for making short deliveries. The company is notified whenever a scooter breaks down, and the problem is classified as being either mechanical or electrical. The company then matches the scooter to the plant where it was assembled. The data table to the right contains a random sample of 200 breakdowns. Use the data file and the relative frequency assessment method to complete parts a through c. Electrical Mechanical Total Plant 1 21 52 73 Plant 2 74 53 127 Total 95 105 200 a. What is the probability a scooter was assembled at Plant 2? P(Plant 2) = (Type an integer or a decimal.) b. What is the probability that a scooter breakdown was due to a mechanical problem? P(mechanical) =D(Type an integer or a decimal.) c. What is the probability that a scooter breakdown was due to an electrical problem and the scooter was assembled at Plant 2? P(electrical and Plant 2) = (Type an integer or a decimal.)

A company produces scooters used by small businesses that find them convenient for making short deliveries. The company is notified whenever a scooter breaks down, and the problem is classified as being either mechanical or electrical. The company then matches the scooter to the plant where it was assembled. The data table to the right contains a random sample of 200 breakdowns. Use the data file and the relative frequency assessment method to complete parts a through c. Electrical Mechanical Total Plant 1 27 44 71 Plant 2 66 63 129 Total 93 107 200 a. What is the probability a scooter was assembled at Plant 2? P(Plant 2) = (Type an integer or a decimal.) b. What is the probability that a scooter breakdown was due to an electrical problem? P(electrical) = (Type an integer or a decimal.) c. What is the probability that a scooter breakdown was due to a mechanical problem and the scooter was assembled at Plant 1? P(mechanical and Plant 1) = (Type an integer or a decimal.)

Empathy: The Interpersonal Reactivity Index is a survey designed to assess four different types of empathy. One type of empathy, called Empathetic Concern measures the tendency to feel sympathy and compassion for people who are less fortunate. The index ranges from 0 (less empathetic) to 28 (more empathet The following data, representing random samples of 11 males and 11 females, are consistent with results reported in psychological studies. Boxplots show tha it is reasonable to assume that the populations are approximately normal. Can you conclude that the mean empathy score for men is less than the mean empathy score for women? Let μ₁ denote the mean empathy score for males and μ₂ denote the mean empathy score for females. Use the a=0.01 level and the critical value method with the table. 12 16 13 26 21 23 8 15 18 25 15 Males 21 23 15 26 25 28 24 16 19 20 23 Females Part 1 of 6 Send data to Excel State the appropriate null and alternate hypotheses. H₁ | M₁ = μ₂ H₁ :|µ₁ <µ₂ This is a…