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 82 students in the highest quartile of the distribution, the mean score was x = 178.90. Assume a population standard deviation of σ = 8.31. These students were all classified as high on their need for closure. Assume that the 82 students represent a random sample of all students who are classified as high on their need for closure. How large a sample is needed if we wish to be 99% confident that the sample mean score is within 2.0 points of the population mean score for students who are high on the need for closure? (Round your answer up to the nearest whole number.)

Answer 1

The following information is provided,
Significance Level, α = 0.01, Margin or Error, E = 2, σ = 8.31

The critical value for significance level, α = 0.01 is 2.58.

The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:
n >= (zc *σ/E)^2
n = (2.58 * 8.31/2)^2
n = 114.92

Therefore, the sample size needed to satisfy the condition n >= 114.92 and it must be an integer number, we conclude that the minimum required sample size is n = 115

Ans : Sample size, n = 115