Question

An existing inventory for a test measuring self-esteem indicates that the scores have a standard deviation of 12. A poychologist gave the self-esteem best to random sample of 100 individuals, and their mean score was 65. Construct a 90% confidence interval for the true mean of all test scores. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to one dedmal place. What is the lower limit of the 90% confidence interval? What is the upper limit of the 90% confidence interval? X ?

Answer 1

Answer to your question is given below

fact, standard deviation (6) = 12 Number of random sample (n) = 100 Sample mean (e) = 65 The 90% confidence interval for true mean is given by, x I Z.0 where, value of a at 90% confidence interval is 1.645. :. 90% confidence interval for true mean is x 1 1.645 6 Jn Lower limit 1.645 o ſn 65 - 1.645 x 12 = 65 -1.974 Jioo Lower limit = 63.026 and, Upper limit x + 1.645 o Jn 65 + 1.645 x 12 65 +1.974 Joo = 66.974 Upper limit The lower and upper limit of gol confidence interval 67.0 respectively. 63.0 and