Question

i cant get this one right. and its not 41.52 i tried that too.

artial Question 6 172 pts In a survey sample of 83 respondents, the mean number of hours worked per week is 39.04, with a standard deviation of 11.51. Calculate a 95% confidence interval for these data. Lower bound: 36.53 Upper bound: 41.55 Answer 1: 36.53 Answer 2: 41.55

Answer 1

Solution: The provided sample mean is X = 39.04 and the sample standard deviation is s = 11.51. The size of the sample is n = 83 and the required confidence level is 95%. The number of degrees of freedom are df = 83 – 1 = 82, and the significance level is a = 0.05. Based on the provided information, the critical t-value for a = 0.05 and df = 82 degrees of freedom is te = 1.989 The 95% confidence for the population mean u is computed using the following expression C1=(x - to + ) Therefore, based on the information provided, the 95% confidence for the population mean u is 1.989 x 11.51 ,39.04 + 1.989 x 11.51 CI= ( 39.04 - 83 783 ) = (39.04 – 2.513, 39.04 +2.513) = (36.527, 41.553)