Question

Three experiments investigating the relation between need for cognitive closure and persuasion were performed. Part of the study involved administering a "need for closure scale" to a group of students enrolled in an introductory psychology course. The "need for closure scale" has scores ranging from 101 to 201. For the 84 students in the highest quartile of the distribution, the mean score was x = 175.30. Assume a population standard deviation of σ = 7.89. These students were all classified as high on their need for closure. Assume that the 84 students represent a random sample of all students who are classified as high on their need for closure. Find a 95% confidence interval for the population mean score μ on the "need for closure scale" for all students with a high need for closure. (Round your answers to two decimal places.)

lower limit
upper limit

A research group conducted an extensive survey of 2898 wage and salaried workers on issues ranging from relationships with their bosses to household chores. The data were gathered through hour-long telephone interviews with a nationally representative sample. In response to the question, "What does success mean to you?" 1636 responded, "Personal satisfaction from doing a good job." Let p be the population proportion of all wage and salaried workers who would respond the same way to the stated question. Find a 90% confidence interval for p. (Round your answers to three decimal places.)

lower limit
upper limit

Answer 1

A) At 95% confidence interval the critical value is z^* = 1.96

The 95% confidence interval for population mean is

+/- z^* *

= 175.3 +/- 1.96 * 7.89/

= 175.3 +/- 1.6873

= 173.6127, 176.9873

= 173.61, 176.99

Lower limit = 173.61

Upper limit = 176.99

B) = 1636/2898 = 0.5645

At 90% confidence interval the critical value is z^* = 1.645

The 90% confidence interval for population proportion is

+/- z^* * sqrt((1 - )/n)

= 0.5645 +/- 1.645 * sqrt(0.5645 * (1 - 0.5645)/2898)

= 0.5645 +/- ​​​0.0152

= 0.5493, 0.5797

= 0.549, 0.580

Lower limit = 0.549

Upper limit = 0.580