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. What are the two rejection regions in a two-tailed test with a level of significance of 0.01 when n>30 and we know the population standard deviation? Test at the 0.01 level of significance that 55% of families who plan to purchase aa home in the country plan to purchase a ranch style home. Ho = 0.55 and H1 at 0.55. A random sample of 400 families results in 228 families wanting a ranch style home. What decision should be made regarding the null hypothesis? A company wants to extend the shelf life of one of their cosmetic products. The average shelf life of the cosmetic product in the past was| 216 days. A sample of 9 of the newly formulated cosmetic products results in the following shelf lives: 215, 217, 218, 219, 216, 217, 217, 218 and 218 days. At a 0.025 level of significance, is there an increase in the shelf life of the newly formulated product? Explain and support your claim. . A survey found that the average labor cost for changing spark plugs at Garage Awas $88.42 and the average labor cost for changing spark plugs Garage B was $80.61. Researchers sample the total labor cost over the past year for this service by randomly choosing 50 bills from each garage. Assume our conditions are met. Garage A has a standard deviation of 5.62 and Garage B has a standard deviation of4.83. If a they choose a 0.05 level of significance. can they conclude that there is a signicant difference in the rates between GarageAand Garage B? Support your conclusion with the necessary values. . Researchers know that the right hand of right-handed people is normally stronger than the left-hand of right-handed people. They guess that the same is not true for left-handed people (that their left hand is stronger) because they live in a \"right-handed world\". 15 left-handed male subjects are tested on the difference between the strength in their left-hand and right-hand. Assuming our conditions are met, and thatt = 1.8, what decision would the researchers make at a 0.05 level of significance? Support your claim with the necessary values. In twin girls it was found that the mean head circumference of the elder sister was 50.23 cm and the mean head circumference of the younger sister is 49.96. The standard deviation of the differences was 1 cm. Find the t-value, the p-value, and determine if there is a significant difference at 5% with regards to head circumference