1. Three experiments investigating the relation between need for cognitive closure and persuasion were performed. Part o

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1. Three experiments investigating the relation between need forcognitive closure and persuasion were performed. Part of the studyinvolved administering a "need for closure scale" to a group ofstudents enrolled in an introductory psychology course. The "needfor closure scale" has scores ranging from 101 to 201. For the 70students in the highest quartile of the distribution, the meanscore was x = 179.10. Assume a population standard deviation of 𝜎 =8.37. These students were all classified as high on their need forclosure. Assume that the 70 students represent a random sample ofall students who are classified as high on their need for closure.Find a 95% confidence interval for the population mean score 𝜇 onthe "need for closure scale" for all students with a high need forclosure. (Round your answers to two decimal places.)
2. Suppose you are told that a 95% confidence interval for theaverage price of a gallon of regular gasoline in your state is from$3.07 to $3.67. Use the fact that the confidence interval for themean is in the form x − E to x + E to compute the sample mean andthe maximal margin of error E. (Round your answers to two decimalplaces.)
3. A research group conducted an extensive survey of 2930 wageand salaried workers on issues ranging from relationships withtheir bosses to household chores. The data were gathered throughhour-long telephone interviews with a nationally representativesample. In response to the question, "What does success mean toyou?" 1552 responded, "Personal satisfaction from doing a goodjob." Let p be the population proportion of all wage and salariedworkers who would respond the same way to the stated question. Finda 90% confidence interval for p. (Round your answers to threedecimal places.) lower limit upper limit Please explain what/howyou're getting the answers, Thanks in advance!